Mathematical Sciences: Liouville Theorems and Regularity of Mappings Minimizing the Lp Norm of the Gradient

这个项目将产生刘维的基本知识 p-极小化映射的定理和正则性 p-超强不稳定流形 大部分拟议工作 是正在进行的研究，继续或扩展以前的 个人工作（例如， 超强不稳定流形）和联合工作的 investigators. 它借鉴了几个领域的技术， 包括微分几何，偏微分 方程、几何测度论、拓扑学和微积分 变化. Dr. S.沃尔特魏将工作的几何方面 非线性椭圆型方程组的解与极小解的正则性; 邱志明博士将研究 黎曼流形 在联合项目中，魏和丘将 继续研究平均变分法， 外在观点作为一种面对和解决 全局非线性分析和几何问题。

This project will yield basic knowledge of Liouville theorems and regularity of p-minimizing maps into p-superstrongly unstable manifolds. Much of the proposed work is ongoing research that continues or extends previous individual work (e.g. regularity of minimizing harmonic maps in to super-strongly unstable manifolds) and joint work of the investigators. It draws on techniques from several areas, including differential geometry, partial differential equations, geometric measure theory, topology and calculus of variations. Dr. S. Walter Wei will work on geometric aspects of nonlinear elliptic systems and the regularity of minimizers; Dr. Chi-Ming Yau will work on Function theoretic properties of Riemannian manifolds. In joint projects, Wei and Yau will continue to study the average variational method from an extrinsic view point as an approach to confront and resolve problems in global nonlinear analysis and geometry.