Topology of three-manifolds with positive -scalar curvature
Authors:
Edward M. Fan
Affiliation:
Department of Mathematics, Princeton University, Princeton, New Jersey 08544-1000
Abstract:
Consider an -dimensional smooth Riemannian manifold with a given smooth measure on it. We call such a triple a Riemannian measure space. Perelman introduced a variant of scalar curvature in his recent work on solving Poincaré's conjecture , where and is the scalar curvature of . In this note, we study the topological obstruction for the -stable minimal submanifold with positive -scalar curvature in dimension three under the setting of manifolds with density.