The Relative Heat Content for Submanifolds in Sub-Riemannian Geometry
Tommaso Rossi1
1 Institut für Angewandte Mathematik, Universität Bonn, Bonn, Germany
Séminaire de théorie spectrale et géométrie, Volume 36 (2019-2021), pp. 191-212

We study the small-time asymptotics of the relative heat content for submanifolds in sub-Riemannian geometry. First, we prove the existence of a smooth tubular neighborhood for submanifolds of any codimension, assuming they do not have characteristic points. Next, we propose a definition of relative heat content for submanifolds of codimension k≥1 and we build an approximation of this quantity, via smooth tubular neighborhoods. Finally, we show that this approximation fails to recover the asymptotic expansion of the relative heat content of the submanifold, by studying an explicit example.

Published online:
DOI: 10.5802/tsg.376

Tommaso Rossi 1

1 Institut für Angewandte Mathematik, Universität Bonn, Bonn, Germany 
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Tommaso Rossi. The Relative Heat Content for Submanifolds in Sub-Riemannian Geometry. Séminaire de théorie spectrale et géométrie, Volume 36 (2019-2021), pp. 191-212. doi: 10.5802/tsg.376

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