I had similar issues with my D34010 and Linux Mint. I was connected to a tv with a max of 1080p, but the max resolution that appeared in Mint was 720p. I manually added the 1080p resolution but when I selected it I got no output. I tried another cable and got the same result. I switched to Windows 7 and the 1920X1080 resolution was there and I could select it, but I kept getting a pop up that I wasn't using the recommended resolution. I tried every solution I could find online, but no luck.
Finally I tried a third cable, one that was listed as HDMI 1.4a, and suddenly everything clicked into place. 1920X1080 was now listed and selectable in Mint and it worked great, and in Windows I no longer got the pop up.
I don't yet have a 4k display so I haven't seen the same issue with 4k, but I'll ask the guys in the lab if they've seen it and if a new cable resolved it.