Hendrik Dierendonck, a second-generation butcher who has become, as he describes it, “world famous in Belgium” for his curated local beef, thinks Europe’s way of raising cattle results in varied and delicious cuts that European consumers prize.

“They want hormone-free, grass-fed,” Mr. Dierendonck explained recently as he cut steaks at a bloody chopping block in his Michelin-starred restaurant, which backs onto the butchery his father started in the 1970s. “They want to know where it came from.”

Strict European Union food regulations, including a ban on hormones, govern Mr. Dierendonck’s work. And those rules could turn into a trade-war sticking point. The Trump administration argues that American meat, produced without similar regulations, is better — and wants Europe to buy more of it, and other American farm products.

“They hate our beef because our beef is beautiful,” Howard Lutnick, the commerce secretary, said in a televised interview last month. “And theirs is weak.”

Questions of beauty and strength aside, the administration is right about one thing: European policymakers are not keen on allowing more hormone-raised American steaks and burgers into the European Union.

India and Pakistan abruptly declared a cease-fire on Saturday after four days of rapidly escalating drone volleys, shelling and airstrikes that appeared to bring the old enemies to the brink of outright war. Hours later, each country accused the other of violating the deal.

The agreement and subsequent reports of cross-border firing came after four dizzying days of strikes by the nuclear-armed rivals that went deep into each other’s territories, and intense shelling on either side of India and Pakistan’s disputed Kashmir border that left many civilians dead, wounded or displaced. Adding to the bewilderment many people felt at the breakneck pace of events, the truce was initially announced not by India or Pakistan but by President Trump on social media.

And it was not clear, as night fell on Saturday, that the cease-fire would take hold in Kashmir, where a terrorist attack last month on the Indian-controlled side killed 26 people and set off the crisis. Cross-border firing was reported in both the Indian- and Pakistani-controlled parts of the region, and India’s foreign secretary, Vikram Misri, told a news conference that there had been “repeated violations” of the agreement.

He accused Pakistan of breaching the agreement and said India would “deal strongly” with the violations and respond.

A spokesman for Pakistan’s foreign ministry later said the country was “committed” to implementing the cease-fire and that its troops were acting responsibly, “notwithstanding the violations being committed by India in some areas.”

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President Trump has floated changing the name of the Persian Gulf to the Arabian Gulf ahead of a trip to the Middle East next week, a move that infuriated Iran and its people.

“I’ll have to make a decision,” Mr. Trump said in the Oval Office on Wednesday. “I don’t want to hurt anybody’s feelings. I don’t know if feelings are going to be hurt.”

This past week, The Associated Press reported that Mr. Trump planned to announce the renaming on his tour of several Arab countries, which have been lobbying for the change for years.

The turquoise blue water has been called the Persian Gulf since at least 550 B.C., when the Persian dynasty of Cyrus the Great ruled an empire that spanned from India to the edges of western Europe. Ancient Persia is now modern-day Iran, and its entire southern coast stretches along the Persian Gulf.

Iran’s governments, going back to the pre-revolution era of the shah, have stoutly defended Persian Gulf as the only legitimate name. So have Iranians inside and outside the country, who view the name as a core part of their national and cultural identity.

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In the eyes of many of his fellow Greenlanders, Jorgen Boassen is a traitor.

A few weeks ago at a dive bar in Nuuk, Greenland’s capital, someone slugged him in the face, sending him to the hospital. But whatever the consequences of his convictions, he insists he isn’t scared.

“The United States has my back,” he said.

Mr. Boassen, 51, a former bricklayer, is a fervid supporter of President Trump. He campaigned for him in the United States and helped coordinate Donald Trump Jr.’s visit to Greenland this year. On his coffee table at home, three pristine MAGA hats occupy a place of honor.

While his championing of the American president — who has vowed to take over Greenland “one way or the other” — has made Mr. Boassen unpopular at home, it has also turned him into an unlikely political player in the Arctic, a region of growing importance in a warming world eager for its untapped resources.

As he lounged on a couch in his apartment on the edge of Nuuk, wearing a pink T-shirt emblazoned with Mr. Trump’s face, his phone buzzed with a stream of texts from journalists and filmmakers who wanted to talk and investors who hoped he was their ticket to riches in Greenland.

In the debate about the future of the world’s largest island, a semiautonomous overseas territory of Denmark, Mr. Boassen has made it his mission to bring Greenland and the United States closer together.

Still, Mr. Boassen noted he “doesn’t always agree” with the American president.

While Mr. Trump wants to claim the island for the United States, Mr. Boassen is pushing instead for a tight security alliance between an independent Greenland and Washington. That has made him one of the most visible Greenlanders agitating to break with Denmark.

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King Charles III was busy last week marking the 80th anniversary of the Allied victory over Nazi Germany and preparing to fly to Canada to open its parliament later this month. But his public schedule was eclipsed yet again by a highly-publicized eruption from his estranged younger son, Prince Harry.

It has become a familiar pattern for the 76-year-old monarch. Two years after his coronation, his reign is shaping up as both eventful and oddly unchanging in its core narrative — that of a beleaguered father managing a messy brood.

Harry’s emotional plea to be reconciled with his family — made in a recent interview with the BBC, in which he mused about how long his cancer-stricken father had left to live — resurfaced bitter ruptures within the royal family, which has yet to find its footing in the still-fledgling Carolean era.

“There is an overhang in the way we see Charles’ reign,” said Ed Owens, a historian who writes about the British monarchy. “It hasn’t really gotten going, nor are we sure how long it will last.”

To be sure, the king has done a lot. Despite undergoing weekly treatments for cancer diagnosed last year, he traveled to France, Australia, Poland and Italy. He found time to curate a playlist for Apple Music (Kylie Minogue and Bob Marley feature), played host at state banquets and posed for portraits.

But Harry’s comments, which came after a legal defeat over his security arrangements in Britain, dragged attention back to the rift that opened in 2020 when he and his wife, Meghan, withdrew from royal life and moved to California.

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In his first formal address to Roman Catholic cardinals, Pope Leo XIV on Saturday said he would continue the work of Pope Francis in steering the church in a more missionary direction, with greater cooperation among church leaders and a closeness to the marginalized.

Leo said he was committed to following a path of modernization and cited a major document that Francis issued in 2013. From that document, Leo highlighted multiple objectives, including “growth in collegiality,” “popular piety,” a “loving care for the least and the rejected,” and “courageous and trusting dialogue with the contemporary world.”

“Francis masterfully and concretely set it forth,” Leo said, referring to the document, called “Evangelii Gaudium.”

The new pope also explained the choice of his name. The previous pope with his name, Leo XIII, issued a document called the “Rerum Novarum,” known in English as “Rights and Duties of Capital and Labor,” in the late 19th century in which he emphasized the church’s right to make assertions about social issues as they related to moral questions.

The document “addressed the social question in the context of the first great industrial revolution,” Leo explained.

Now, the pope added, another industrial revolution was taking place in the field of artificial intelligence. That, he said, would “pose new challenges for the defense of human dignity, justice and labor.”

The church, he said, “offers to everyone the treasury of her social teaching in response.”

The reference to Francis’ document was not the only endorsement that the new pope gave of his predecessor. Francis, Leo noted, was a “humble servant of God and of his brothers and sisters” who gave an “example of complete dedication to service and to sober simplicity of life.”

After the pope’s address, some of the cardinals also made speeches. Dominik Duka, a cardinal from Prague, said the subject of some of the speeches was the theme of “synodality” — referring to the process of dialogue between church leaders and lay people that was one of Pope Francis’ signature legacies.

Cardinal Duka said there had also been mention of the Vatican’s relationship with China. During his papacy, Francis made a deal with Beijing in the hopes of bolstering the church’s presence there.

The cardinals appeared to have noted the message about maintaining the direction set by Francis’ papacy.

As he exited the meeting, Cardinal Baltazar Enrique Porras Cardozo of Venezuela said the pope “spoke about the continuity of the pontificate of Francis and then he asked some questions to us.” Those questions were “mostly about the formation of priests and bishops,” the cardinal added.

On his way out of the meeting, Cardinal Sean Brady of Ireland said Leo was in the process of “greeting everybody now, which is very nice.”

On Saturday, after the meeting, Leo made an unannounced visit to Our Lady of Good Counsel in Genazzano, an Augustinian sanctuary outside Rome. A cheering crowd greeted him as he exited the passenger’s seat of a black minivan. Residents of the town leaned out of windows to take a picture of the pope as Leo shook hands and waved to those gathered.

Later on, he paid a visit to St. Mary Major, where Pope Francis is buried. He stood in front of his predecessor’s simple marble tomb. Before kneeling in front of it in prayer, he laid a white rose on it.

Jason Horowitz and Elizabeth Dias contributed reporting from Vatican City.

Most American burgers are, in fact, not entirely American.

The patties grilled at backyard barbecues or flipped in fast-food restaurants are often a blend of ground beef, both homegrown and imported from other countries, especially Brazil. In school cafeterias and home kitchens, this global mix of beef is seared, fried and sizzled into millions of tacos, meatballs and lasagnas every day.

Now, President Trump’s dismantling of the global trading system through his imposition of broad-based tariffs is leading to shifts in commerce that could make winners out of countries like Brazil that produce commodities the world covets.

When it comes to beef — crucial to satisfying Americans’ hunger for cheap cuts of meat — tariffs will make Brazilian beef more expensive.

But at the same time, Brazil is suddenly a more appealing source for China, another enormous consumer of beef, because its trade war with the United States — and the high tariffs the two nations have imposed on each other — has left China looking for other countries with ample supplies of inexpensive meat.

While U.S. meatpackers, most likely anticipating escalating prices, have been stocking up on Brazilian beef in recent weeks, according to trade data, Brazilian beef exports to China also increased in April.

As a result, prices for commodity beef from Brazil have increased by about 20 percent since early April, trade experts say.

“The moment, from our point of view, has never been more favorable to Brazil,” said Luiz Gustavo Oliveira, the vice president of Grupo Fribal, a Brazilian meat company. “And the world has its doors open to Brazilian meat.”

U.S. meat processors, on the other hand, are struggling to grapple with higher beef prices and what they mean for their bottom lines and how much their customers will be asked to pay.

In a bid to keep prices down, Kent Sander, whose family owns a meat-processing business in rural Indiana, has begun mixing pork, which is less expensive, into the beef burgers he sells. “I’m trying to give people an affordable option,” he said.

Brazil is the world’s biggest exporter of beef, having surpassed the United States in the past 20 years. With vast swaths of farmland where enormous cattle herds can graze, and lower labor and other related costs, Brazilian ranchers have conquered the global market by producing beef on a larger scale and far more cheaply than its competitors.

China and the United States are the top two buyers of Brazilian beef, with both countries sharply increasing their purchases in recent years to keep up with growing domestic appetites for lean, inexpensive meat that neither country’s farmers can satisfy.

“Brazil is in a unique position,” Roberto Perosa, the president of the Brazilian Association of Meat Exporting Industries and a former trade secretary for the Brazilian government. “No other country in the world can meet this demand.”

While the United States is still the world’s biggest producer of beef, its cattle — fattened up on a soy or corn diet — is better suited for expensive, marbled steaks famous for their rich flavor, according to U.S. industry experts.

Some of this cattle is slaughtered to produce cheaper cuts of beef. But a large portion is turned into premium steaks like filet mignon or rib-eye, which are consumed at home and at steakhouses, or exported to the rest of the world. China, the third-largest buyer of U.S. beef, imported $1.6 billion worth of meat in 2024.

To churn out the cheaper ground beef that many Americans eat daily, U.S. meatpackers mix fattier, local beef with leaner, grass-fed varieties from abroad.

“Not all beef is equal,” said Glynn Tonsor, a professor of agricultural economics at Kansas State University. “And in the U.S., we consume more ground beef than we produce.”

To meet the demand, the United States increased its beef imports from Brazil from 2023 to 2024 by more than 50 percent, reaching a record $1.3 billion.

But Brazilian beef is now subject to the 10 percent tariff Mr. Trump applied on just about every U.S. trading partner, and the longer the tariffs persist, the more likely they are to reshape the global beef trade in lasting ways.

President Luiz Inácio Lula da Silva of Brazil said recently that he did not want to “make a choice” between China and the United States, the nation’s two largest trading partners.

“I want to negotiate with everyone,” said Mr. Lula, who is scheduled to visit China this month. “I want to sell and buy.”

But Mr. Lula’s top foreign policy adviser, Celso Amorim, told a Brazilian newspaper that China now offers Brazil “more opportunities and fewer risks” than the United States.

And after China revoked the export licenses of more than 390 U.S. meat-processing companies in retaliation for U.S. tariffs, Brazil’s agricultural minister said the Latin American country was eager to fill the gap.

“Someone will need to supply this meat, which was supplied by the Americans,” said the minister, Carlos Fávaro.

In China, a long-held preference for cheaper pork has been giving way to a newfound taste for steaks and beef hot pots in recent years, as the country’s middle class has grown.

Chinese beef imports rose from less than $100 million in 2010 to over $13 billion in 2024, with the country buying nearly half of its beef from Brazil last year.

Most Brazilian beef was already subject to steep U.S. tariffs, first put in place in the 1990s to shield American cattle ranchers from a flood of cheaper imported beef. Now, Mr. Trump’s recent tariffs have pushed the levy to 36 percent. By comparison, Brazilian beef faces tariffs of only 12 percent in China.

With China mostly halting U.S. beef imports, supply chains for “this commodity have been completely shaken,” said André Ferreira, a Brazil-based maritime transport specialist at DMS Logistics. “So China will look at Brazil differently now.”

Some Brazilian beef producers are already charting ambitious plans for the future.

For Grupo Fribal, which raises, slaughters and packages beef for domestic and international markets, business has been booming in recent years, as exports to China and the United States have surged.

Now, the company plans to increase its cattle herd to 60,000 from 40,000 by next year, in part to take advantage of even stronger demand spurred by tariffs. “The moment is now,” said Mr. Oliveira of Grupo Fribal.

But breeding, raising and fattening more cattle for beef takes time and money, making such plans a long-term bet that demand will continue growing.

Brazil, an immense nation with a mild climate favoring agriculture, has more cattle than people. Since the 1970s, both large-scale ranching and family farming have spread across every region of the country, including the Amazon rainforest.

Still, back-to-back droughts have taken a toll, with Brazil’s beef production expected to shrink by nearly 5 percent in 2025, according to Safras & Mercado, a consultancy.

And even if some Brazilian ranchers are able to increase production in the short term, they may struggle to ship more beef abroad as major Brazilian ports are already operating near full capacity.

In the United States, trade experts say American farmers will be hard pressed to replace beef imports from Brazil and were wrestling with other challenges before the tariffs. U.S. cattle inventories have fallen to a 73-year low, partly because of drought and rising costs of animal feed.

Demand for cheaper beef is expected to increase as economic jitters pull U.S. consumers away from expensive cuts and toward burgers, pushing up prices. Ground beef prices in U.S. cities have climbed 43 percent over the past five years, according to the U.S. Bureau of Labor Statistics.

Even with tariffs, the United States will most likely continue relying on Brazilian beef because there is no other similarly large source for the American market, experts said.

This may be good news for Brazil’s cattle ranchers, said Mr. Perosa, of the meat exporting association, but not for U.S. consumers. “It’s American society that will have to foot the bill,” he said.