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Alexandrov spaces with
maximal radius
Karsten Grove and Peter Petersen |
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Geometry & Topology 26 (2022) 1635–1668
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Abstract |
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We prove several rigidity theorems related to and including Lytchak’s problem. The focus is on Alexandrov spaces with , nonempty boundary and maximal radius . We exhibit many such spaces that indicate that this class is remarkably flexible. Nevertheless, we also show that, when the boundary is either geometrically or topologically spherical, it is possible to obtain strong rigidity results. In contrast to this, one can show that with general lower curvature bounds and strictly convex boundary only cones can have maximal radius. We also mention some connections between our problems and the positive mass conjectures. |
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Keywords
Alexandrov geometry, rigidity, boundary convexity
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Mathematical Subject Classification 2010
Primary: 53C20, 53C24
Secondary: 53C23
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References |
Publication
Received: 4 March 2020
Revised: 5 April 2021
Accepted: 7 May 2021
Published: 28 October 2022
Proposed: Paul Seidel
Seconded: John Lott, Dmitri Burago
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Authors |
| Karsten Grove | |
| Department of Mathematics University of Notre Dame Notre Dame, IN United States |
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| Peter Petersen | |
| Department of Mathematics University of California, Los Angeles Los Angeles, CA United States |
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