In this paper we investigate the small time heat kernel asymptotics on the cut locus on a class of surfaces of revolution, which are the simplest two-dimensional Riemannian manifolds different from the sphere with non-trivial cut-conjugate locus. We determine the degeneracy of the exponential map near a cut-conjugate point and present the consequences of this result to the small time heat kernel asymptotics at this point. These results give a first example where the minimal degeneration of the asymptotic expansion at the cut locus is attained.
@article{AIHPC_2014__31_2_281_0, author = {Barilari, Davide and Jendrej, Jacek}, title = {Small time heat kernel asymptotics at the cut locus on surfaces of revolution}, journal = {Annales de l'I.H.P. Analyse non lin\'eaire}, pages = {281--295}, publisher = {Elsevier}, volume = {31}, number = {2}, year = {2014}, doi = {10.1016/j.anihpc.2013.03.003}, mrnumber = {3181670}, zbl = {1301.53035}, language = {en}, url = {http://www.numdam.org/articles/10.1016/j.anihpc.2013.03.003/} }
TY - JOUR AU - Barilari, Davide AU - Jendrej, Jacek TI - Small time heat kernel asymptotics at the cut locus on surfaces of revolution JO - Annales de l'I.H.P. Analyse non linéaire PY - 2014 SP - 281 EP - 295 VL - 31 IS - 2 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.anihpc.2013.03.003/ DO - 10.1016/j.anihpc.2013.03.003 LA - en ID - AIHPC_2014__31_2_281_0 ER -
%0 Journal Article %A Barilari, Davide %A Jendrej, Jacek %T Small time heat kernel asymptotics at the cut locus on surfaces of revolution %J Annales de l'I.H.P. Analyse non linéaire %D 2014 %P 281-295 %V 31 %N 2 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.anihpc.2013.03.003/ %R 10.1016/j.anihpc.2013.03.003 %G en %F AIHPC_2014__31_2_281_0
Barilari, Davide; Jendrej, Jacek. Small time heat kernel asymptotics at the cut locus on surfaces of revolution. Annales de l'I.H.P. Analyse non linéaire, Volume 31 (2014) no. 2, pp. 281-295. doi : 10.1016/j.anihpc.2013.03.003. http://www.numdam.org/articles/10.1016/j.anihpc.2013.03.003/
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