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2022 Alexandrov spaces with maximal radius
Karsten Grove, Peter Petersen
Geom. Topol. 26(4): 1635-1668 (2022). DOI: 10.2140/gt.2022.26.1635

Abstract

We prove several rigidity theorems related to and including Lytchak’s problem. The focus is on Alexandrov spaces with curv1, nonempty boundary and maximal radius π2. 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.

Citation

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Karsten Grove. Peter Petersen. "Alexandrov spaces with maximal radius." Geom. Topol. 26 (4) 1635 - 1668, 2022. https://doi.org/10.2140/gt.2022.26.1635

Information

Received: 4 March 2020; Revised: 5 April 2021; Accepted: 7 May 2021; Published: 2022
First available in Project Euclid: 11 November 2022

Digital Object Identifier: 10.2140/gt.2022.26.1635

Subjects:
Primary: 53C20 , 53C24
Secondary: 53C23

Keywords: Alexandrov geometry , boundary convexity , rigidity

Rights: Copyright © 2022 Mathematical Sciences Publishers

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Vol.26 • No. 4 • 2022
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