Harmonic Forms and Topology of Complete Manifolds

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.