Riesz transforms on forms and -Hodge decomposition on complete Riemannian manifolds

  • Xiang-Dong Li

    Chinese Academy of Sciences, Beijing, China

Abstract

In this paper we prove the Strong -stability of the heat semigroup generated by the Hodge Laplacian on complete Riemannian manifolds with non-negative Weitzenböck curvature. Based on a probabilistic representation formula, we obtain an explicit upper bound of the -norm of the Riesz transforms on forms on complete Riemannian manifolds with suitable curvature conditions. Moreover, we establish the Weak -Hodge decomposition theorem on complete Riemannian manifolds with non-negative Weitzenböck curvature.

A correction to this paper is available.

Cite this article

Xiang-Dong Li, Riesz transforms on forms and -Hodge decomposition on complete Riemannian manifolds. Rev. Mat. Iberoam. 26 (2010), no. 2, pp. 481–528

DOI 10.4171/RMI/607