Some Gradient Estimates on Covering Manifolds

Nick Dungey

Displaying similar documents to “Some Gradient Estimates on Covering Manifolds”

Large time behaviour of heat kernels on non-compact manifolds: fast and slow decays

Thierry Coulhon (1998)

Journées équations aux dérivées partielles

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In this talk we shall present some joint work with A. Grigory’an. Upper and lower estimates on the rate of decay of the heat kernel on a complete non-compact riemannian manifold have recently been obtained in terms of the geometry at infinity of the manifold, more precisely in terms of a kind of $L^{2}$ isoperimetric profile. The main point is to connect the decay of the $L^{1} - L^{\infty}$ norm of the heat semigroup with some adapted Nash or Faber-Krahn inequalities, which is done by functional analytic methods....

Some remarks on gradient estimates for heat kernels.

Dungey, Nick (2006)

Abstract and Applied Analysis

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Heat kernels on non-compact riemannian manifolds : a partial survey

Thierry Coulhon (1996-1997)

Séminaire de théorie spectrale et géométrie

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Comparing heat operators through local isometries or fibrations

Manlio Bordoni (2000)

Bulletin de la Société Mathématique de France

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Riesz meets Sobolev

Thierry Coulhon, Adam Sikora (2010)

Colloquium Mathematicae

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We show that the $L^{p}$ boundedness, p > 2, of the Riesz transform on a complete non-compact Riemannian manifold with upper and lower Gaussian heat kernel estimates is equivalent to a certain form of Sobolev inequality. We also characterize in such terms the heat kernel gradient upper estimate on manifolds with polynomial growth.