NEW YORK — Broadway, Carnegie Hall, and Lincoln Center all remained dark Tuesday as Superstorm Sandy left the New York entertainment industry fighting to go on with the show — even if it meant performing for empty studios.

That was how David Letterman and Jimmy Fallon taped their late shows Monday night, leading to some remarkably quiet monologues. On Tuesday, as the city took account of the storm damage, some late-night shows were moving back into full production, while the aftermath of Sandy continued to cause the cancellations of film premieres, film and TV production, and even that most unshakable performer: Bruce Springsteen.