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The Journal of Geometric Analysis

, Volume 16, Issue 4, pp 597–631 | Cite as

Sobolev inequalities for differential forms andL q,p -cohomology

  • Vladimir Gol’dshtein
  • Marc Troyanov
Article

Abstract

We study the relation between Sobolev inequalities for differential forms on a Riemannian manifold (M, g) and the Lq,p-cohomology of that manifold.

The Lq,p-cohomology of (M,g) is defined to be the quotient of the space of closed differential forms in Lp(M) modulo the exact forms which are exterior differentials of forms in Lq (M).

Math Subject Classifications

58J10 58A12 46E35 35J15 

Key Words and Phrases

Sobolev inequality differential forms Lq,p-cohomology 

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Copyright information

© Mathematica Josephina, Inc. 2006

Authors and Affiliations

  1. 1.Department of MathematicsBen Gurion University of the NegevBeer ShevaIsrael
  2. 2.Institut de Géométrie, algèbre et topologie (IGAT) Bâtiment BCHÉcole Polytechnique Féderale de LausanneLausanneSwitzerland

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