In this article, 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 by-product, 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 nongeneric case, a cornucopia of asymptotics can occur, even for Riemannian surfaces.

On the Heat Diffusion for Generic Riemannian and Sub-Riemannian Structures

Barilari D.;Boscain U.;
2017

Abstract

In this article, 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 by-product, 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 nongeneric case, a cornucopia of asymptotics can occur, even for Riemannian surfaces.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11577/3368982
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