Harmonic Forms and Topology of Complete Manifolds

University Of Minnesota-Twin Cities, Minneapolis MN

Investigators

Abstract

DMS-0404817 P.I.: Jiaping Wang, University of Minnesota-Twin Cities Title: Harmonic forms and topology of complete manifolds ABSTRACT This proposed project is about relating the analysis and topology on complete noncomapct manifolds. In particular, it is proposed to search for an extension of the de Rham-Hodge theory, and to relate the spectrum of the Hodge Laplacian to the topology of manifolds. The main objective of this project is to describe some large scale structures of objects which are high dimensional analogue of the unbounded surfaces. The approach is to inspect the physical steady states of a naturally defined energy on such objects. The results and techniques are expected to be useful in describing more complicated systems arising from physics, biology and other branches of science.