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. © 2013 Elsevier Masson SAS. All rights reserved.

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

Barilari D.;
2014

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. © 2013 Elsevier Masson SAS. All rights reserved.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11577/3401940
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