Though he has been front-and-center in public life for more than four decades in the country’s cultural capital, Mr. Trump has left a meager trail to suggest what positions he might take on public arts funding and arts education, along with issues like censorship and economic policies that would affect creative industries, not to mention how he and the first lady, Melania Trump, might decorate the White House.

His authoritarian stance during the campaign — including threats to “open up libel laws” to allow journalists to be “sued like you’ve never got sued before” and a tweet calling for an end to “Saturday Night Live” because of its parody of him — suggest freedom of expression could come under assault in his administration. But then, his actions during the campaign and long before it in the real-estate world strongly indicate that if such expression were not directed toward Mr. Trump personally, he might not spend much time caring about it.

“I don’t see anything apocalyptic with him coming in,” said Rocco Landesman, the Broadway impresario and former chairman of the National Endowment for the Arts, which disburses grants to cultural organizations and projects. “The Tea Party has a real grievance with the arts, and when I was at the N.E.A., during the budgeting process, the Tea Party conservatives would X out the budget, and we’d have to fight to restore it. But I would not envision that kind of process with President Trump at all. That doesn’t seem to be his agenda.”

Mr. Trump has been vague about his position on government funding for the arts and humanities and for arts-related education. His hard-line position on immigration has some arts groups with an international focus worried about visa issues, which have already become more difficult in recent years. And Mr. Trump has also proposed reducing tax benefits for charitable giving, which could have a far more devastating impact on the arts than cuts in public money, which has been declining for many years in inflation-adjusted dollars.

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Art dealers said they had never seen Mr. Trump at an auction and had no sense of his taste in art or the degree to which he collects. A 1997 profile in The New Yorker by Mark Singer related an anecdote about Mr. Trump’s effort to have a statue of Columbus slightly taller than the Statue of Liberty erected near the Riverside South development on the Upper West Side. (The statue never came to the city.) “It’s got forty million dollars’ worth of bronze in it,” Mr. Trump said of the work, by a critically derided Georgian-born Russian sculptor, Zurab Tsereteli, whom Mr. Trump called “major and legit.”

Mr. Trump’s two brief public turns that concerned works of art were not promising for art lovers. In 1980, he began demolition of the old Bonwit Teller department store to build Trump Tower, and though he had promised important Art Deco limestone bas-reliefs from the building to the Metropolitan Museum of Art, workers destroyed the reliefs. Mr. Trump, pretending to be a Trump spokesman named “John Baron,” later claimed in an interview with The New York Times that the reliefs were “without artistic merit.”

In 1999, after Mayor Rudolph W. Giuliani threatened to cut off city funding to the Brooklyn Museum because of an exhibition featuring a painting by the British artist Chris Ofili that depicted a Virgin Mary figure and incorporated collaged pornographic elements and clumps of dried elephant dung, Mr. Trump joined in the criticism. Then exploring a run for president as a candidate of the Reform Party, Mr. Trump praised Mr. Giuliani’s attempt to block public funding for the museum. He called Mr. Ofili’s work and that of some other artists “absolutely gross, degenerate stuff,” and vowed as president to ensure that federal funds would never support such art.