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Metric-measure inequalities in sub-Riemannian manifolds

Total Cost €


EC-Contrib. €






 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.

laplacian    kernel    spaces    backgrounds    respectively    informations    sr    solutions    equation    impulse    context    stochastic    arising    endowed    qualitative    supervisor    presenting    amounting    deepen    sub    point    employed    space    adjointness    encoding    gecomethods    2016    smooth    framework    conjectured    boscain    interaction    group    opposite    generalizations    variational    allowed    expansion    metric    theoretic    estimates    theory    usually    frame    region    isoperimetric    heisenberg    donne    le    suitable    shape    original    dynamics    erc    received    follow    proving    naturally    completeness    heat    self    operators    literature    quantum    prove    dynamical    conjecture    techniques    stg    geomeg    singularities    thanks    hypoelliptic    manifolds    confinement    geometric    2010    innovative    riemannian    pansu    inequalities    singular    functional    view    2017    action    relations    class    particles    underlying    mesur    intrinsic    novelty    obtain    geometry    pi   

Project "MesuR" data sheet

The following table provides information about the project.


Organization address
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


Take a look of project's partnership.

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


 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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The information about "MESUR" are provided by the European Opendata Portal: CORDIS opendata.

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