Curvature bounds and heat kernelsdiscrete versus continuous spaces
discrete versus continuous spaces
dc.contributor.advisor | Sturm, Karl-Theodor | |
dc.contributor.author | Bonciocat, Anca-Iuliana | |
dc.date.accessioned | 2020-04-12T16:49:11Z | |
dc.date.available | 2020-04-12T16:49:11Z | |
dc.date.issued | 2008 | |
dc.identifier.uri | https://hdl.handle.net/20.500.11811/3659 | |
dc.description.abstract | We introduce and study rough (approximate) lower curvature bounds and rough curvature-dimension conditions for discrete spaces and for graphs. These notions extend the ones introduced in \cite{St06a} and \cite{St06b} to a larger class of non-geodesic metric measure spaces. They are stable under an appropriate notion of convergence in the sense that the metric measure space which is approximated by a sequence of discrete spaces with rough curvature $\geq K$ will have curvature $\geq K$ in the sense of \cite{St06a}. Moreover, in the converse direction, discretizations of metric measure spaces with curvature $\geq K$ will have rough curvature $\geq K$. We apply our results to concrete examples of homogeneous planar graphs. We derive perturbed transportation cost inequalities, that imply mass concentration and exponential integrability of Lipschitz maps. For spaces that satisfy a rough curvature-dimension condition we prove a generalized Brunn-Minkowski inequality and a Bonnet-Myers type theorem. | en |
dc.language.iso | eng | |
dc.rights | In Copyright | |
dc.rights.uri | http://rightsstatements.org/vocab/InC/1.0/ | |
dc.subject.ddc | 510 Mathematik | |
dc.title | Curvature bounds and heat kernels | |
dc.title.alternative | discrete versus continuous spaces | |
dc.type | Dissertation oder Habilitation | |
dc.publisher.name | Universitäts- und Landesbibliothek Bonn | |
dc.publisher.location | Bonn | |
dc.rights.accessRights | openAccess | |
dc.identifier.urn | https://nbn-resolving.org/urn:nbn:de:hbz:5N-14976 | |
ulbbn.pubtype | Erstveröffentlichung | |
ulbbnediss.affiliation.name | Rheinische Friedrich-Wilhelms-Universität Bonn | |
ulbbnediss.affiliation.location | Bonn | |
ulbbnediss.thesis.level | Dissertation | |
ulbbnediss.dissID | 1497 | |
ulbbnediss.date.accepted | 12.07.2008 | |
ulbbnediss.fakultaet | Mathematisch-Naturwissenschaftliche Fakultät | |
dc.contributor.coReferee | Beznea, Lucian |
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