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On symmetric transformations in metric measured geometry

By Gerardo Sosa Garciamarín


The central objects of study in this thesis are metric measure spaces. These are metric spaces which are endowed with a reference measure and enriched with basic topological, geometric and measure theoretical properties. The objective of the first part of the work is to characterize metric measure spaces whose symmetry groups admit a differential structure making them Lie groups. The second part is concerned with the analysis of the induced geometry of spaces admitting non-trivial symmetries. More in detail, it is shown that in many cases synthetic notions of Ricci curvature lower bounds are inherited by quotient spaces

Topics: metric measure spaces, Ricci curvature, symmetric transformations, optimal transport, info:eu-repo/classification/ddc/500, ddc:500
Year: 2017
OAI identifier: oai:qucosa:de:qucosa:16754
Provided by: Qucosa
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