Volume Growth and Positive Scalar Curvature
by
Guihua Gong
University of Puerto Rico, Rio Piedras
Coauthors: Guoliang Yu (University of Colorado)

Gromov conjectured that a uniformly contractible complete Riemannian manifold can not have uniformly positive scalar curvature. We will prove the conjecture provided that the manifold has subexponential volume growth. The above conjecture is a consequence of coarse Baum-Connes conjecture which can be used to compute the higher index of the Dirac operator of the Riemannian manifold. We prove the coarse Baum-Connes conjecture for the corresponding case.

Date received: May 9, 1999

Copyright © 1999 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cacw-68.