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, p. 281-295
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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},
     publisher = {Elsevier},
     volume = {31},
     number = {2},
     year = {2014},
     pages = {281-295},
     doi = {10.1016/j.anihpc.2013.03.003},
     zbl = {1301.53035},
     mrnumber = {3181670},
     language = {en},
     url = {http://www.numdam.org/item/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/item/AIHPC_2014__31_2_281_0/

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