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 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.
@article{TSG_2019-2021__36__191_0, author = {Tommaso Rossi}, title = {The {Relative} {Heat} {Content} for {Submanifolds} in {Sub-Riemannian} {Geometry}}, journal = {S\'eminaire de th\'eorie spectrale et g\'eom\'etrie}, pages = {191--212}, publisher = {Institut Fourier}, address = {Grenoble}, volume = {36}, year = {2019-2021}, doi = {10.5802/tsg.376}, language = {en}, url = {https://proceedings.centre-mersenne.org/articles/10.5802/tsg.376/} }
TY - JOUR AU - Tommaso Rossi TI - The Relative Heat Content for Submanifolds in Sub-Riemannian Geometry JO - Séminaire de théorie spectrale et géométrie PY - 2019-2021 SP - 191 EP - 212 VL - 36 PB - Institut Fourier PP - Grenoble UR - https://proceedings.centre-mersenne.org/articles/10.5802/tsg.376/ DO - 10.5802/tsg.376 LA - en ID - TSG_2019-2021__36__191_0 ER -
%0 Journal Article %A Tommaso Rossi %T The Relative Heat Content for Submanifolds in Sub-Riemannian Geometry %J Séminaire de théorie spectrale et géométrie %D 2019-2021 %P 191-212 %V 36 %I Institut Fourier %C Grenoble %U https://proceedings.centre-mersenne.org/articles/10.5802/tsg.376/ %R 10.5802/tsg.376 %G en %F TSG_2019-2021__36__191_0
Tommaso Rossi. The Relative Heat Content for Submanifolds in Sub-Riemannian Geometry. Séminaire de théorie spectrale et géométrie, Tome 36 (2019-2021), pp. 191-212. doi : 10.5802/tsg.376. https://proceedings.centre-mersenne.org/articles/10.5802/tsg.376/
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