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Isoperimetric inequalities and capacities on Riemannian manifolds

  • Alexander Grigor’yan
Part of the Operator Theory: Advances and Applications book series (OT, volume 109)

Abstract

We discuss extensions of some results of V.G.Maz’ya to Riemannian manifolds. His proofs of the relationships between capacities, isoperimetric inequalities and Sobolev inequalities did not use specific properties of the Euclidean space. His method, transplanted to manifolds, gives a unified approach to such results as parabolicity criteria, eigenvalues estimates, heat kernel estimates, etc.

Keywords

Riemannian Manifold Heat Kernel Sobolev Inequality Isoperimetric Inequality Geodesic Ball 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Basel AG 1999

Authors and Affiliations

  • Alexander Grigor’yan
    • 1
  1. 1.Department of MathematicsImperial CollegeLondonUK

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