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Benjamini-Schramm Convergence of Normalized Characteristic Numbers of Riemannian Manifolds

dc.contributor.advisorSchick, Thomas Prof. Dr.
dc.contributor.authorLuckhardt, Daniel
dc.date.accessioned2020-04-30T08:33:42Z
dc.date.available2020-04-30T08:33:42Z
dc.date.issued2020-04-30
dc.identifier.urihttp://hdl.handle.net/21.11130/00-1735-0000-0005-1388-C
dc.identifier.urihttp://dx.doi.org/10.53846/goediss-7955
dc.identifier.urihttp://dx.doi.org/10.53846/goediss-7955
dc.language.isoengde
dc.rights.urihttp://creativecommons.org/licenses/by-nc-nd/4.0/
dc.subject.ddc510de
dc.titleBenjamini-Schramm Convergence of Normalized Characteristic Numbers of Riemannian Manifoldsde
dc.typedoctoralThesisde
dc.contributor.refereeSchick, Thomas Prof. Dr.
dc.date.examination2018-06-05
dc.description.abstractengWe study a weak form of Gromov-Hausdorff convergence of Riemannian manifolds, also known as Benjamini-Schramm convergence. This concept is also applicable to other areas and has widely been studied in the context of graphs. The main result is the continuity of characteristic numbers normalized by the volume with respect to the Benjamini-Schramm topology on the class of Riemannian manifolds with a uniform lower bound on injectivity radius and Ricci curvature. An immediate consequence is a comparison theorem that gives for any characteristic number a linear bound in terms of the volume on the entire class of manifolds mentioned. We give another interpretation of the result showing that characteristic numbers can be reconstructed with some accuracy from local random information.de
dc.contributor.coRefereeMeyer, Ralf Prof. Dr.
dc.contributor.thirdRefereeHuckemann, Stephan Prof. Dr.
dc.contributor.thirdRefereeLuke, Russell Prof. Dr.
dc.contributor.thirdRefereePidstrygach, Viktor Prof. Dr.
dc.contributor.thirdRefereeWitt, Ingo Prof. Dr.
dc.subject.engBenjamini-Schramm convergencede
dc.subject.engRiemannian manifoldde
dc.subject.engcharacteristic numberde
dc.subject.engGromov-Hausdorff convergencede
dc.subject.engmetric measure spacesde
dc.identifier.urnurn:nbn:de:gbv:7-21.11130/00-1735-0000-0005-1388-C-6
dc.affiliation.instituteFakultät für Mathematik und Informatikde
dc.subject.gokfullMathematics (PPN61756535X)de
dc.identifier.ppn1696982804


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