Geometric Analysis

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Nonlinear partial differential equations arise naturally in the study of physical phenomena . We propose to study some of these equations related to problems in geometry. These lead to challenging questions in nonlinear differential equations which points to the direction of geometric analysis. Our objective is to develop various analytic tools for these equations, investigate structures of geometric solutions, qualitative properties of solutions, and derive geometric and topological consequences. Advances in the theory of these equations will lead to the solutions of the proposed problems in geometry, will enrich the existing theory of fully nonlinear partial differential equations in general, with applications in heat type flows and nonlinear equations in plasma and material science.