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Heat Content Asymptotic in sub-Riemannian Manifolds

Speaker: 
Tommaso Rossi
Institution: 
Institut Fourier and SISSA
Schedule: 
Tuesday, December 10, 2019 - 16:00
Location: 
A-135
Abstract: 

We study the short-time asymptotic of the sub-Riemannian heat content for a smoothly bounded domain in any sub-Riemannian manifold. We show that, in a wide range of situations, the heat content admits a complete asymptotic expansion as a function of square root of t, whose coefficients, in the classical spirit of spectral geometry, contain geometrical information of the domain. Moreover, we provide an inductive formula for computing the coefficients of the expansion, showing that hey can be approximated by their Riemannian counterparts. Our asymptotic formula generalizes prior works by A. Savo in the Riemannian setting and by J. Tyson, J. Wang in the first Heisenberg group.
This is a joint work with my advisor, Luca Rizzi.

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