You can't checkmate with just a king and knight. Isolating into a corner won't help, as the king can not get close enough to keep the opposing king "in place", and while the knight can try to keep the king cornered, there would be no positions where the knight can check where the checked king can't escape the check by safely moving towards the knight.

EDIT: There would be positions where you don't try position the king to try to hold the opposing king in a corner where the opposing king can't move towards the knight to escape a check, but in those positions it will be able to move away in other directions.