Small time heat kernel asymptotics at the cut locus on surfaces of revolution

  • Davide Barilari

    CMAP UMR 7641, École Polytechnique CNRS, Route de Saclay, 91128 Palaiseau, France, Equipe INRIA GECO Saclay-Île-de-France, Paris, France
  • Jacek Jendrej

    CMAP UMR 7641, École Polytechnique CNRS, Route de Saclay, 91128 Palaiseau, France

Abstract

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.

Cite this article

Davide Barilari, Jacek Jendrej, Small time heat kernel asymptotics at the cut locus on surfaces of revolution. Ann. Inst. H. Poincaré Anal. Non Linéaire 31 (2014), no. 2, pp. 281–295

DOI 10.1016/J.ANIHPC.2013.03.003