Geometric Analysis

非线性偏微分方程是在研究物理现象时自然产生的。我们建议研究一些与几何问题有关的方程。这些都为非线性微分方程的研究带来了新的挑战，为几何分析指明了方向。我们的目标是为这些方程开发各种分析工具，研究几何解的结构，解的定性性质，并导出几何和拓扑后果。这些方程理论的进展将导致几何问题的解决方案，将丰富现有的完全非线性偏微分方程理论，在热型流动和等离子体和材料科学中的非线性方程的应用。

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.