Manhattan still has some of the highest apartment rents in the U.S., but rents are growing much more slowly — especially for the most expensive, new apartments. Developers have opened so many new apartment buildings, that the number of vacant apartments has begun to rise, and property managers are beginning to offer deals to attract residents.

Some luxury developments are offering as much as four months free rent on a two-year lease. Despite these concessions, some apartments linger vacant for months.

Developers opened 11,514 new rental units last year in Manhattan and Brooklyn. Another 13,340 are planned to open this year, according to Citi Habitats, a real estate brokerage. That should keep the pressure on all of the apartments that are priced at that high level.