Mathematical Sciences: Existence of Many Minimal Surfaces onRiemannian Manifolds and Applications in Geometry and Topology

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The research entails studies of analytic and topological properties of classes of minimal surfaces in Riemannian manifolds of dimension greater than or equal to 3. The methods are primarily those of geometric measure theory and are expected to achieve further insight to the analytic and topological structures of hypersurfaces lying in these manifolds. Particular attention will be paid to dimension 3 where new techniques are applied to show that certain Riemann surfaces can be realized as minimal types.