Gas cook top and diagonal floor cab.

I am thinking of putting a diagonal floor cab in the 90 degree corner. The gas cook top comes down a few inches and I would have to cut the top of the side wall of the cabinets. I do not believe that the few inches the cook top comes down would interfere with a lazy Susan. The cook top would protrude into the diagonal cab about 5-6 in. The cook top will be 30 in and I will be putting granite as a counter top. If the side cab is cut would there be enough support for the granite at that spot.Yes the cab under the cook top would not be centered with the cook top. Trying to do the best I can with the limited space.