An almost isometric sphere theorem and weak strainers on Alexandrov spaces

  title={An almost isometric sphere theorem and weak strainers on Alexandrov spaces},
  author={Qingsong Cai},
  journal={Indiana University Mathematics Journal},
  • Qingsong Cai
  • Published 2017
  • Mathematics
  • Indiana University Mathematics Journal
In this paper we define a weak (n+1,ε)−strainer on an Alexandrov space with curvature ≥ 1, and prove an almost isometric sphere theorem in the setting of a weak strainer, making use of a rigidity theorem f or round spheres. To prove the rigidity theorem we investigate several proper ties of weak strainers, e.g. the maximality property, the covering property of the balls centered at strainer points, and an equilibrium property of a maximal ly separated weak strainer. At last we study several… 
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