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$L^{2}$ -invariants of locally symmetric spaces.

Olbrich, Martin (2002)

Documenta Mathematica

$L^{2}$ -preserving Schrödinger heat flow under the Ricci flow.

Wang, Linfeng (2010)

Balkan Journal of Geometry and its Applications (BJGA)

$L^{p} - L^{q}$ estimates for functions of the Laplace-Beltrami operator on noncompact symmetric spaces. III

Michael Cowling, Saverio Giulini, Stefano Meda (2001)

Annales de l’institut Fourier

Let $X$ be a symmetric space of the noncompact type, with Laplace–Beltrami operator $- ℒ$ , and let $[b, \infty)$ be the $L^{2} (X)$ -spectrum of $ℒ$ . For $τ$ in $ℂ$ such that $Re τ \geq 0$ , let $𝒫_{τ}$ be the operator on $L^{2} (X)$ defined formally as $\exp (- τ {(ℒ - b)}^{1 / 2})$ . In this paper, we obtain $L^{p} - L^{q}$ operator norm estimates for $𝒫_{τ}$ for all $τ$ , and show that these are optimal when $τ$ is small and when $| \arg τ |$ is bounded below $π / 2$ .

$L^{p}$ pinching and compactness theorems for compact riemannian manifolds

Deane Yang (1987/1988)

Séminaire de théorie spectrale et géométrie

La trace du noyau de la chaleur des variétés hyperboliques de dimension 3

Józef Dodziuk (1995/1996)

Séminaire de théorie spectrale et géométrie

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 $L^{1} - L^{\infty}$ norm of the heat semigroup with some adapted Nash or Faber-Krahn inequalities, which is done by functional analytic methods. We shall...

Large time estimates for non-symmetric heat kernel on the affine group

Camillo Melzi (2002)

Annales mathématiques Blaise Pascal

Leading terms in the heat invariants for the Laplacians of the De Rham signature, and spin complexes.

P.B. Gilkey, T.P. Branson, B. Orsted (1990)

Mathematica Scandinavica

Lefschetz formulae for arithmetic varieties.

Mark Stern (1994)

Inventiones mathematicae

L'équation de la chaleur associée à la courbure de Ricci

Jean Pierre Bourguignon (1985/1986)

Séminaire Bourbaki

Lie Groups and KdV Equations.

Shiing-shen Chern, Chia-kuei Peng (1979)

Manuscripta mathematica

L'inégalité de Penrose

Marc Herzlich (2000/2001)

Séminaire Bourbaki

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

Thierry Coulhon, Xuan Thinh Duong, Xiang 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...

Long-time existence for a solution of the equation of evolution of harmonic maps into an ellipsoid.

Thierry Horsin Molinaro (1993)

Manuscripta mathematica

Lower bounds on //K...//1...... For some contractions K of L² (...), with applications to Markov operators.

Francoise Lust-Piquard (1995)

Mathematische Annalen

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