Function Theory and Topology of Complete Manifolds

University Of Minnesota-Twin Cities, Minneapolis MN

Investigators

Abstract

DMS-0072181 Jiaping Wang In this project, the principal investigator proposes to study the interactions between the symmetries of a complete manifold and the behaviors of various analytical objects on it. More specifically, he proposes to link the structure and the size of the covering group with the polynomial growth harmonic functions and the spectral data on the covering space. The main objectives of this project include deriving topological information about a (noncompact) manifold via analytical approaches and furthering the understanding of how the symmetries of the space affect the behavior of solutions to various geometric differential equations, which is one of the main themes of the geometric analysis. This project is intended to study how the behavior of the solutions to differential equations is related to the global structure and shape of the underlying space with partial symmetries. It is expected to both enhance our understanding of the geometric-analytic structure and have direct implications to various fields including possible applications in industry.