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Topological and Geometric Rigidity for Spaces with Curvature Bounded Below

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Recent Advances in Alexandrov Geometry

Part of the book series: CIMAT Lectures in Mathematical Sciences ((CIMATLMS))

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Abstract

We briefly survey two results asserting topological and geometric rigidity of certain classes of spaces with curvature bounded below: The Borel Conjecture for irreducible and sufficiently collapsed Alexandrov 3-spaces and the Maximal Volume Entropy Rigidity of R C D (−(N − 1), N)-spaces.

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Acknowledgements

JNZ is supported by a DGAPA-UNAM postdoctoral scholarship. This manuscript is partially based on the talk given by the author at the 11th mini-meeting in Differential Geometry at the Centro de Investigación en Matemáticas (CIMAT). He wishes to thank the organizers for the opportunity to submit this expository article and Chris Connell for very useful communications. The author further wishes to thank the anonymous reviewer for a careful reading of the manuscript.

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Núñez-Zimbrón, J. (2022). Topological and Geometric Rigidity for Spaces with Curvature Bounded Below. In: Arizmendi Echegaray, G., Hernández-Lamoneda, L., Herrera Guzmán, R. (eds) Recent Advances in Alexandrov Geometry. CIMAT Lectures in Mathematical Sciences. Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-99298-9_3

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