Displaying similar documents to “A geometric approach to on-diagonal heat kernel lower bounds on groups”

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 ∞ norm of the heat semigroup with some adapted Nash or Faber-Krahn inequalities, which is done by functional analytic methods....

Analysis on Extended Heisenberg Group

B. Zegarliński (2011)

Annales de la faculté des sciences de Toulouse Mathématiques

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In this paper we study Markov semigroups generated by Hörmander-Dunkl type operators on Heisenberg group.

Continuous Measures on Homogenous Spaces

Michael Björklund, Alexander Fish (2009)

Annales de l’institut Fourier

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In this paper we generalize Wiener’s characterization of continuous measures to compact homogenous manifolds. In particular, we give necessary and sufficient conditions on probability measures on compact semisimple Lie groups and nilmanifolds to be continuous. The methods use only simple properties of heat kernels.

Heat kernel upper bounds on a complete non-compact manifold.

Alexander Grigor'yan (1994)

Revista Matemática Iberoamericana

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Let M be a smooth connected non-compact geodesically complete Riemannian manifold, Δ denote the Laplace operator associated with the Riemannian metric, n ≥ 2 be the dimension of M. Consider the heat equation on the manifold ut - Δu = 0, where u = u(x,t), x ∈ M, t > 0. The heat kernel p(x,y,t) is by definition the smallest positive fundamental solution to the heat equation which exists on any manifold (see [Ch],...