Small time heat kernel asymptotics at the cut locus on surfaces of revolution
Analysis of PDEs
2013-03-14 v2 Differential Geometry
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 2-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.
Keywords
Cite
@article{arxiv.1211.1811,
title = {Small time heat kernel asymptotics at the cut locus on surfaces of revolution},
author = {Davide Barilari and Jacek Jendrej},
journal= {arXiv preprint arXiv:1211.1811},
year = {2013}
}
Comments
Accepted on Annales IHP - Analyse Non Lineaire