Trace heat kernel asymptotics in 3D contact sub-Riemannian geometry

By Davide Barilari. 2011

67 citations recorded by the source corpus.

In this paper, we study the small time asymptotics for the heat kernel on a sub-Riemannian manifold, using a perturbative approach. We explicitly compute, in the case of a 3D contact structure, the first two coefficients of the small time asymptotics expansion of the heat kernel on the diagonal, expressing them in terms of the two basic functional invariants χand κ defined on a 3D contact structure.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/515c1794e279e80b3784c60432105bf1e18730b9

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In Applied Mathematics

In Computational Theory and Mathematics

In Mathematical Physics

Citations in the corpus

A Comprehensive Introduction to Sub-Riemannian Geometry (2019, methodology): “, for Pt(q, q)) and their relation with the Hausdorff dimension were studied in [BA89, BAL91], see also [Bar13].”
Small time heat kernel asymptotics at the sub-Riemannian cut locus (2012, background): “The problem of relating the sub-Riemannian distance to the heat-kernel is an old problem (see for instance [6, 13, 18, 21, 22, 23, 30, 36, 38, 39, 44, 50, 52]).”
The subelliptic heat kernel on the CR sphere (2011, background): “formula for the sub-Riemannian distance. To put things in perspective let us observe that the study of explicit expressions for subelliptic heat kernels has generated a great amount of work (see [1], [2] [4], [3], [5] [7], [11] and the references therein). The motivations for ﬁnding explicit formula”
A Formula for Popp’s Volume in Sub-Riemannian Geometry (2012, background): “This is a second order differential operator, which has been studied in [3, 5].”