If the position is left as it is at the end of the game, the white group is dead and the black group is alive. The black group has plenty of liberties, so White cannot capture it before the corner group dies. As always -- the main point of the complication of the rules -- the external ko threat makes no difference, since during the resolution of life and death after the game one can not recapture a ko until one has passed (for that particular ko), so Black can carry through the capture of the white group, simply answering the would-be ko threats if White plays them.
The best play during the game -- again, this is not a matter for the rules -- is for White to fill the liberties of the black group. When it is down to 6 liberties, Black will have to carry out the capture of the corner. Now White _can_ use the external ko threats, since this is happening during the game; the ko, with the black and white groups both at stake, is slightly bigger than the ko threats, so Black should ignore the first ko threat and win the ko. Compared with leaving the position as it is, White is better off by the value of the ko threat and its followup, less 7 points because White has played 7 more extra stones than Black in the corner.