The City of New York has agreed to contribute $17 million to the project. Mr. Diller, with his wife, Diane von Furstenberg, will cover the remaining expense — “whatever it costs,” Mr. Diller said. (The latest estimate is $130 million.) Mr. Diller has also promised to maintain Pier 55 and run the amphitheater for 20 years. The Hudson River Park Trust plans to complete construction in 2018, but civic groups asked a court in June to halt construction until the project undergoes a new environmental review and is approved by the Legislature.