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MesuR SIGNED

Metric-measure inequalities in sub-Riemannian manifolds

Total Cost €

0

EC-Contrib. €

0

Partnership

0

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 MesuR project word cloud

Explore the words cloud of the MesuR project. It provides you a very rough idea of what is the project "MesuR" about.

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Project "MesuR" data sheet

The following table provides information about the project.

Coordinator
SORBONNE UNIVERSITE 

Organization address
address: 21 RUE DE L'ECOLE DE MEDECINE
city: PARIS
postcode: 75006
website: n.a.

contact info
title: n.a.
name: n.a.
surname: n.a.
function: n.a.
email: n.a.
telephone: n.a.
fax: n.a.

 Coordinator Country France [FR]
 Total cost 173˙076 €
 EC max contribution 173˙076 € (100%)
 Programme 1. H2020-EU.1.3.2. (Nurturing excellence by means of cross-border and cross-sector mobility)
 Code Call H2020-MSCA-IF-2017
 Funding Scheme MSCA-IF-EF-ST
 Starting year 2019
 Duration (year-month-day) from 2019-09-01   to  2021-08-31

 Partnership

Take a look of project's partnership.

# participants  country  role  EC contrib. [€] 
1    SORBONNE UNIVERSITE FR (PARIS) coordinator 173˙076.00

Map

 Project objective

The goal of MesuR is to deepen our knowledge of geometric and dynamical properties of a class of metric-measure spaces, called sub-Riemannian (sR) manifolds. These are generalizations of Riemannian manifolds, naturally arising in the frame of control theory and hypoelliptic operators. SR geometry is a theory in expansion, and it recently received a great impulse thanks to two ERC-StG on this topic: “GeCoMethods” (2010-2016, PI: U. Boscain), and “GeoMeG” (2017–now, PI: E. Le Donne). In this action we focus on sR manifolds endowed with intrinsic measures. These have been introduced in the frame of geometric control theory: as a key novelty, they are allowed here to have singularities, opposite to the smooth measures usually employed in the existing literature on geometry and analysis in sR manifolds. In this framework, we aim at proving: (1) sR isoperimetric inequalities for singular measures, and investigate relations with the standing Pansu’s conjecture about the shape of isoperimetric sets in the Heisenberg group; (2) Essential self-adjointness and stochastic completeness of the intrinsic sR Laplacian, amounting to prove the conjectured confinement of the heat and of quantum particles to the non-singular region; (3) Heat kernel estimates, i.e., qualitative informations on the solutions to the Heat equation for the intrinsic sR Laplacian. Our objectives will follow by proving suitable functional inequalities encoding geometric properties of the underlying space, that we call metric-measure inequalities. This will be done thanks to an original interaction between variational and control theoretic techniques, respectively typical of the backgrounds of the applicant and of the Supervisor. Through this innovative point of view, we will obtain new results in the context of sR geometry and provide new techniques to study geometry and dynamics on metric-measure spaces presenting singularities.

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