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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.

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

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

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