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

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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.