Published Paper

Inserted: 11 oct 2013
Last Updated: 16 apr 2021

Journal: Int. Math. Res. Not.
Year: 2017
Doi: https://doi.org/10.1093/imrn/rnw141

Abstract:

In this paper we provide the small-time heat kernel asymptotics at the cut locus in three relevant cases: generic low-dimensional Riemannian manifolds, generic 3D contact sub-Riemannian manifolds (close to the starting point) and generic 4D quasi-contact sub-Riemannian manifolds (close to a generic starting point). As a byproduct, we show that, for generic low-dimensional Riemannian manifolds, the only singularities of the exponential map, as a Lagragian map, that can arise along a minimizing geodesic are A₃ and A₅ (in the classification of Arnol'd's school). We show that in the non-generic case, a cornucopia of asymptotics can occur, even for Riemannian surfaces.

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• BBCN-heat.pdf