Asymptotiques en temps petit du noyau de la chaleur des métriques riemanniennes et sous-riemanniennes

Davide Barilari; Ugo Boscain; Grégoire Charlot; Robert W. Neel

doi:10.5802/tsg.294

Davide Barilari ¹; Ugo Boscain ¹; Grégoire Charlot ²; Robert W. Neel ³

¹ CNRS, CMAP Ecole Polytechnique and equipe INRIA GECO Saclay-Île-de-France, Paris, France
² Institut Fourier, UMR 5582, Université Grenoble 1 and equipe INRIA GECO Saclay-Île-de-France, Paris, France
³ Department of Mathematics, Lehigh University, Bethlehem, PA, USA

Séminaire de théorie spectrale et géométrie, Volume 31 (2012-2014), pp. 55-70.

Abstract
Résumé

Abstract. We provide the small-time asymptotics of the heat kernel at the cut locus in three cases: generic Riemannian manifolds in dimension less or equal to 5, generic 3D contact and 4D quasi-contact sub-Riemannian manifolds (close to the starting point). As a byproduct we show that, for generic Riemannian manifolds of dimension less or equal to 5, the only possible singularities of the exponential map along a minimizing geodesic are $A_{3}$ and $A_{5}$ .

Nous établissons l’asymptotique en temps petit du noyau de la chaleur au lieu de coupure dans les situations génériques, en géométrie riemannienne en dimension inférieure ou égale à 5, en géométrie sous-riemannienne de contact en dimension 3 ou de quasi-contact en dimension 4. La preuve nous permet de montrer qu’en dimension inférieure ou égale à 5 les seules singularités d’une application exponentielle riemannienne générique qui peuvent apparaître le long d’une géodésique minimisante sont $A_{3}$ et $A_{5}$ .

DOI: 10.5802/tsg.294

Author's affiliations:

Davide Barilari ¹; Ugo Boscain ¹; Grégoire Charlot ²; Robert W. Neel ³

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     author = {Davide Barilari and Ugo Boscain and Gr\'egoire Charlot and Robert W. Neel},
     title = {Asymptotiques en temps petit du noyau de la chaleur des m\'etriques riemanniennes et sous-riemanniennes},
     journal = {S\'eminaire de th\'eorie spectrale et g\'eom\'etrie},
     pages = {55--70},
     publisher = {Institut Fourier},
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Davide Barilari; Ugo Boscain; Grégoire Charlot; Robert W. Neel. Asymptotiques en temps petit du noyau de la chaleur des métriques riemanniennes et sous-riemanniennes. Séminaire de théorie spectrale et géométrie, Volume 31 (2012-2014), pp. 55-70. doi : 10.5802/tsg.294. https://tsg.centre-mersenne.org/articles/10.5802/tsg.294/

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