Radius Estimates for Alexandrov Space with Boundary

Abstract

In this note, we study the radius of a positively curved or nonnegatively curved Alexandrov space with strictly convex boundary, the convexity of which is measured by the Base-Angle defined by Alexander and Bishop. As an application of the radius estimates, we derive several rigidity theorems, which can be thought as extensions of a recent result of Grove–Petersen.

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Acknowledgements

The authors would like to thank Stephanie Alexander and Yuguang Shi for their interest in our work and helpful discussions. The first author would like to thank Karsten Grove for communications and discussions on the radius estimates. The authors would like to thank the anonymous referee for careful reading of our manuscript and several helpful suggestions.

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Correspondence to Jian Ge.

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J. Ge is partially supported by NSFC 11731001.

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Ge, J., Li, R. Radius Estimates for Alexandrov Space with Boundary. J Geom Anal 31, 619–630 (2021). https://doi.org/10.1007/s12220-019-00292-2

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Keywords

  • Alexandrov space
  • Riemannian manifold
  • Radius
  • Rigidity

Mathematics Subject Classification

  • Primary 53C23
  • 53C20