Heat kernels on non-compact riemannian manifolds : a partial survey
Thierry Coulhon (1996-1997)
Séminaire de théorie spectrale et géométrie
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Thierry Coulhon (1996-1997)
Séminaire de théorie spectrale et géométrie
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Thierry Coulhon, Adam Sikora (2010)
Colloquium Mathematicae
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We show that the 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.
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 isoperimetric profile. The main point is to connect the decay of the norm of the heat semigroup with some adapted Nash or Faber-Krahn inequalities, which is done by functional analytic methods....
Nick Dungey (2004)
Bulletin of the Polish Academy of Sciences. Mathematics
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Let M be a complete Riemannian manifold which is a Galois covering, that is, M is periodic under the action of a discrete group G of isometries. Assuming that G has polynomial volume growth, we provide a new proof of Gaussian upper bounds for the gradient of the heat kernel of the Laplace operator on M. Our method also yields a control on the gradient in case G does not have polynomial growth.
Manlio Bordoni (2000)
Bulletin de la Société Mathématique de France
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A. ter Elst, Derek Robinson, Adam Sikora (1998)
Colloquium Mathematicae
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We consider pure mth order subcoercive operators with complex coefficients acting on a connected nilpotent Lie group. We derive Gaussian bounds with the correct small time singularity and the optimal large time asymptotic behaviour on the heat kernel and all its derivatives, both right and left. Further we prove that the Riesz transforms of all orders are bounded on the Lp -spaces with p ∈ (1, ∞). Finally, for second-order operators with real coefficients we derive matching Gaussian...
Ewa Damek (1997)
Colloquium Mathematicae
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Georgios Alexopoulos, Noël Lohoué (1994)
Bulletin de la Société Mathématique de France
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Pascal Auscher, Thierry Coulhon, Xuan Thinh Duong, Steve Hofmann (2004)
Annales scientifiques de l'École Normale Supérieure
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