Any way to put Mac mini to sleep remotely?
I'm pretty sure you can do this with a hot-corner and the built-in VNC server. (You would need a VNC viewer for iOS, there are LOTS of them.

You could also create an applescript:
tell application "System Events" to sleep
and run it using the VNC connection.



Alternatively, you can turn on ssh, ssh in, and issue the command:
pmset sleepnow (See the pmset man page)
to put the mac to sleep.

This would require a ssh client for iOS. Again, there are a LOT of them. Personally, I have used iSSH, and it works fine.



As @mankoff stated in a comment, RowMote states in it's store description:


  
  SLEEP AND WAKE: Put your Mac to sleep by holding the Play button for 3 seconds while controlling any Apple application, just like the
  hardware remote. Rowmote automatically wakes up sleeping machines
  which are connected via Ethernet!