MacBook Air mid 2011 external Display resoltion > 1080p which adapter? I want to use my new 27" Display in full resolution. I've tried two different cheap mini displayport to hdmi adapters but they only work with a max resolution of 1080p.
Do I really need an expensive Mini DisplayPort to Dual-Link-DVI-adapter or should i try a mini displayport to displayport adapter to get the full 2560x1440 resolution?
Mac OS X should detect the supported resolutions when you connect the display. Your problem might indeed be related to the adapter and cable you are using. According to the HDMI 1.4 spec, standard HDMI cables only support resolutions up to 1080i.

I suggest you use the DisplayPort or DVI port on your monitor instead, and buy the appropriate adapter for one of those.