Sobolev inequalities for differential forms and L q,p -cohomology

Vladimir Gol'Dshtein; Marc Troyanov

doi:10.1007/BF02922133

Sobolev inequalities for differential forms and L _q,p -cohomology

Vladimir Gol'Dshtein, Marc Troyanov

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

39 Scopus citations

Abstract

We study the relation between Sobolev inequalities for differential forms on a Riemannian manifold (M, g) and the L _q,p-cohomology of that manifold. The L _q,p-cohomology of (M,g) is defined to be the quotient of the space of closed differential forms in L ^p(M) modulo the exact forms which are exterior differentials of forms in L ^q (M).

Original language	English
Pages (from-to)	597-631
Number of pages	35
Journal	Journal of Geometric Analysis
Volume	16
Issue number	4
DOIs	https://doi.org/10.1007/BF02922133
State	Published - 1 Dec 2006

Keywords

L -cohomology
Sobolev inequality
differential forms

ASJC Scopus subject areas

Geometry and Topology

Access to Document

10.1007/BF02922133

Cite this

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abstract = "We study the relation between Sobolev inequalities for differential forms on a Riemannian manifold (M, g) and the L q,p-cohomology of that manifold. The L q,p-cohomology of (M,g) is defined to be the quotient of the space of closed differential forms in L p(M) modulo the exact forms which are exterior differentials of forms in L q (M).",

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AU - Troyanov, Marc

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N2 - We study the relation between Sobolev inequalities for differential forms on a Riemannian manifold (M, g) and the L q,p-cohomology of that manifold. The L q,p-cohomology of (M,g) is defined to be the quotient of the space of closed differential forms in L p(M) modulo the exact forms which are exterior differentials of forms in L q (M).

AB - We study the relation between Sobolev inequalities for differential forms on a Riemannian manifold (M, g) and the L q,p-cohomology of that manifold. The L q,p-cohomology of (M,g) is defined to be the quotient of the space of closed differential forms in L p(M) modulo the exact forms which are exterior differentials of forms in L q (M).

KW - L -cohomology

KW - Sobolev inequality

KW - differential forms

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