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June, 2010 Riesz transforms on forms and $L^p$-Hodge decomposition on complete Riemannian manifolds
Xiang-Dong Li
Rev. Mat. Iberoamericana 26(2): 481-528 (June, 2010).

Abstract

In this paper we prove the Strong $L^p$-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 $L^p$-norm of the Riesz transforms on forms on complete Riemannian manifolds with suitable curvature conditions. Moreover, we establish the Weak $L^p$-Hodge decomposition theorem on complete Riemannian manifolds with non-negative Weitzenböck curvature.

Citation

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Xiang-Dong Li . "Riesz transforms on forms and $L^p$-Hodge decomposition on complete Riemannian manifolds." Rev. Mat. Iberoamericana 26 (2) 481 - 528, June, 2010.

Information

Published: June, 2010
First available in Project Euclid: 4 June 2010

zbMATH: 1197.53052
MathSciNet: MR2677005

Subjects:
Primary: 53C21 , 58J65
Secondary: 58J40 , 60J65

Keywords: Hodge decomposition , martingale transforms , Riesz transforms , Weitzenböck curvature

Rights: Copyright © 2010 Departamento de Matemáticas, Universidad Autónoma de Madrid

Vol.26 • No. 2 • June, 2010
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