Asymptotiques en temps petit du noyau de la chaleur des métriques riemanniennes et sous-riemanniennes
Séminaire de théorie spectrale et géométrie, Tome 31 (2012-2014) , pp. 55-70.

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 .

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 .

@article{TSG_2012-2014__31__55_0,
     author = {Barilari, Davide and Boscain, Ugo and Charlot, Gr\'egoire and Neel, Robert W.},
     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},
     address = {Grenoble},
     volume = {31},
     year = {2012-2014},
     doi = {10.5802/tsg.294},
     language = {fr},
     url = {http://archive.numdam.org/articles/10.5802/tsg.294/}
}
Barilari, Davide; Boscain, Ugo; Charlot, Grégoire; Neel, Robert W. Asymptotiques en temps petit du noyau de la chaleur des métriques riemanniennes et sous-riemanniennes. Séminaire de théorie spectrale et géométrie, Tome 31 (2012-2014) , pp. 55-70. doi : 10.5802/tsg.294. http://archive.numdam.org/articles/10.5802/tsg.294/

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