Minimal hypersurfaces in U(m)-invariant scalar flat Kähler manifolds

In this thesis, we study minimal hypersurfaces with U(m)-invariant Kähler metrics. We provide new method to construct AE scalar flat Kähler manifolds which contains stable minimal hypersurface. The computation of the ADM mass and area has been completed but it is in the process of verification. Once the computation of the mass is verified, I will add in the final version of this thesis, the proof of the Penrose Inequality for U(m)-invariant Kähler manifolds in dimension four.