THE DIAMAGNETIC INEQUALITY FOR THE HEAT SEMIGROUP IN HERMITIAN BUNDLES OVER COMPACT RIEMANNIAN MANIFOLDS

Author:

,MUST˘AT, EA ALEXANDRU

Abstract

This article presents a geometric-flavoured proof of the diamagnetic inequality for the heat semigroup in a Hermitian bundle based on Chernoff’s theorem about the approximation of contraction semigroups in Banach spaces.

Publisher

Editura Academiei Romane

Reference9 articles.

1. "[1] I. Chavel, Eigenvalues in Riemannian Geometry. Pure and Applied Mathematics 115, Academic Press, Orlando, 1984.

2. [2] I. Chavel, Riemannian Geometry. A Modern Introduction, Second Edition. Cambridge Stud. Adv. Math. 98, Cambridge Univ. Press, Cambridge, 2006.

3. [3] E.B. Davies, One-Parameter Semigroups. London Math. Soc., Monographs, 15, Academic Press, London, 1980.

4. [4] B. Driver and A. Thalmaier, Heat equation derivative formulas for vector bundles. J. Funct. Anal. 183, 1, 42-108.

5. [5] A. Grigor'yan, Heat Kernel and Analysis on Manifolds. AMS/IP Studies in Advanced Mathematics 47, American Mathematical Society (AMS), Providence, 2009.

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