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dc.contributor.author
Gigli, Nicola
dc.contributor.author
Mondino, Andrea
dc.contributor.author
Savaré, Giuseppe
dc.date.accessioned
2017-06-11T03:23:18Z
dc.date.available
2017-06-11T03:23:18Z
dc.date.issued
2013-11-19
dc.identifier.uri
http://hdl.handle.net/20.500.11850/78561
dc.description.abstract
Aim of this paper is to discuss convergence of pointed metric measure spaces in absence of any compactness condition. We propose various definitions, show that all of them are equivalent and that for doubling spaces these are also equivalent to the well known measured-Gromov-Hausdorff convergence. Then we show that the curvature conditions $CD(K,\infty)$ and $RCD(K,\infty)$ are stable under this notion of convergence and that the heat flow passes to the limit as well, both in the Wasserstein and in the $L^2$-framework. We also prove the variational convergence of Cheeger energies in the naturally adapted $\Gamma$-Mosco sense and the convergence of the spectra of the Laplacian in the case of spaces either uniformly bounded or satisfying the $RCD(K,\infty)$ condition with $K>0$. When applied to Riemannian manifolds, our results allow for sequences with diverging dimensions.
dc.language.iso
en
dc.publisher
ETH Zürich, Forschungsinstitut für Mathematik
dc.title
Convergence of pointed non-compact metric measure spaces and stability of Ricci curvature bounds and heat flows
dc.type
Working Paper
ethz.pages.start
arXiv:1311.4907
ethz.size
62 p.
ethz.notes
Submitted on 19 Nov 2013.
ethz.publication.place
Zürich
ethz.publication.status
published
ethz.leitzahl
ETH Zürich::00002 - ETH Zürich::00012 - Lehre und Forschung::00007 - Departemente::02000 - Dep. Mathematik / Dep. of Mathematics::02003 - Mathematik Selbständige Professuren::03600 - Rivière, Tristan / Rivière, Tristan
ethz.leitzahl.certified
ETH Zürich::00002 - ETH Zürich::00012 - Lehre und Forschung::00007 - Departemente::02000 - Dep. Mathematik / Dep. of Mathematics::02003 - Mathematik Selbständige Professuren::03600 - Rivière, Tristan / Rivière, Tristan
ethz.date.deposited
2017-06-11T03:23:23Z
ethz.source
ECIT
ethz.identifier.importid
imp5936517e5ea5079841
ethz.ecitpid
pub:123584
ethz.eth
yes
ethz.availability
Metadata only
ethz.rosetta.installDate
2017-07-17T10:19:43Z
ethz.rosetta.lastUpdated
2018-11-02T12:54:10Z
ethz.rosetta.versionExported
true
ethz.COinS
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