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 et .
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 and .
@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://www.numdam.org/articles/10.5802/tsg.294/} }
TY - JOUR AU - Barilari, Davide AU - Boscain, Ugo AU - Charlot, Grégoire AU - Neel, Robert W. TI - Asymptotiques en temps petit du noyau de la chaleur des métriques riemanniennes et sous-riemanniennes JO - Séminaire de théorie spectrale et géométrie PY - 2012-2014 SP - 55 EP - 70 VL - 31 PB - Institut Fourier PP - Grenoble UR - http://www.numdam.org/articles/10.5802/tsg.294/ DO - 10.5802/tsg.294 LA - fr ID - TSG_2012-2014__31__55_0 ER -
%0 Journal Article %A Barilari, Davide %A Boscain, Ugo %A Charlot, Grégoire %A Neel, Robert W. %T Asymptotiques en temps petit du noyau de la chaleur des métriques riemanniennes et sous-riemanniennes %J Séminaire de théorie spectrale et géométrie %D 2012-2014 %P 55-70 %V 31 %I Institut Fourier %C Grenoble %U http://www.numdam.org/articles/10.5802/tsg.294/ %R 10.5802/tsg.294 %G fr %F TSG_2012-2014__31__55_0
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://www.numdam.org/articles/10.5802/tsg.294/
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