Currently displaying 1 – 12 of 12

Showing per page

Order by Relevance | Title | Year of publication

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

Thierry Coulhon — 1998

Journées équations aux dérivées partielles

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. We shall...

Riesz meets Sobolev

Thierry CoulhonAdam Sikora — 2010

Colloquium Mathematicae

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.

Absence de principe du maximum pour certaines équations paraboliques complexes

Pascal AuscherThierry CoulhonPhilippe Tchamitchian — 1996

Colloquium Mathematicae

Le but de cette note est de montrer que le principe du maximum, même dans une version affaiblie, n’est pas vérifıé pour la classe des opérateurs paraboliques du type d / d t + L , où L est un opérateur différentiel elliptique d’ordre 2 sous forme divergence à coefficients complexes mesurables et bornés en dimension supérieure ou égale à 5. Le principe de démonstration repose sur un résultat abstrait de la théorie des semi-groupes permettant d’utiliser le contre-exemple présenté dans [MNP] à la régularité des...

A geometric approach to on-diagonal heat kernel lower bounds on groups

Thierry CoulhonAlexander Grigor'yanChristophe Pittet — 2001

Annales de l’institut Fourier

We introduce a new method for obtaining heat kernel on-diagonal lower bounds on non- compact Lie groups and on infinite discrete groups. By using this method, we are able to recover the previously known results for unimodular amenable Lie groups as well as for certain classes of discrete groups including the polycyclic groups, and to give them a geometric interpretation. We also obtain new results for some discrete groups which admit the structure of a semi-direct product or of a wreath product....

Littlewood-Paley-Stein functions on complete Riemannian manifolds for 1 ≤ p ≤ 2

Thierry CoulhonXuan Thinh DuongXiang Dong Li — 2003

Studia Mathematica

We study the weak type (1,1) and the L p -boundedness, 1 < p ≤ 2, of the so-called vertical (i.e. involving space derivatives) Littlewood-Paley-Stein functions and ℋ respectively associated with the Poisson semigroup and the heat semigroup on a complete Riemannian manifold M. Without any assumption on M, we observe that and ℋ are bounded in L p , 1 < p ≤ 2. We also consider modified Littlewood-Paley-Stein functions that take into account the positivity of the bottom of the spectrum. Assuming that...

Page 1

Download Results (CSV)