L^p-Cohomology, Heat Semigroup and Stratified Spaces

Abstract

Let (M, g) be an incomplete Riemannian manifold of finite volume and let 2le p<infty . In the first part of this paper we prove that under certain assumptions the inclusion of the space of L^p-differential forms into that of L^2-differential forms gives rise to an injective/surjective map between the corresponding L^p and L^2 cohomology groups. Then in the second part we provide various applications of these results to the curvature and the intersection cohomology of compact Thom–Mather stratified pseudomanifolds and complex projective varieties with only isolated singularities.