Geodesics and Laplace spectrum on 3D contact sub-Riemannian manifolds: the Reeb flow

Abstract: Joint work with Luc Hillairet (Orléans) and Emmanuel Trélat (Paris). A 3D closed manifold with a contact distribution and a metric on it carries a canonical contact form. The associated Reeb flow plays a central role for the asymptotics of the geodesics and for the spectral asymptotics of the Laplace operator. I plan to describe it using some Birkhoff normal forms.

analysis of PDEsdifferential geometrymetric geometryoptimization and controlspectral theory

Audience: researchers in the topic

( video )

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Sub-Riemannian Seminars

Series comments: The "Sub-Riemannian seminars" are the union of the "Séminaire de géométrie et analyse sous-riemannienne" (held in Paris since 2011) and the "International Sub-Riemannian Seminars", which were born in spring 2020 as a reaction to the COVID-19 pandemic.

The new format will gather every 3 weeks on average, alternating between these types of sessions:

- physical session in Paris (Laboratoire Jacques-Louis Lions), also transmitted online on Zoom.

- fully online session on Zoom.

- special session hosted physically somewhere else, and transmitted online.

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