On the Yamabe Problem on Riemannian Manifolds with
Rough Metrics
Ali Behzadan
UCSD
Abstract:
We state the Yamabe conjecture and briefly review the techniques that have been used to study the Yamabe
problem on Riemannian manifolds with smooth metrics. We review some of the basic tools from functional
analysis and the theory of partial differential equations for studying the problem in the case of manifolds
with non-smooth metrics. In particular, we will discuss some important results related to the Yamabe
problem for closed manifolds and asymptotically Euclidean manifolds with rough metrics.