A rigidity phenomenon on Riemannian manifolds with reverse volume pinching

  • Peihe WangEmail author
  • Yuliang Wen
Original Paper


In the article stated here, we introduce the Hausdorff convergence to discuss the differentiable sphere theorem with some curvature conditions and volume pinching. Finally, a type of rigidity phenomenon on Riemannian manifolds will be derived.


Volume Comparison Theorem Hausdorff convergence Differentiable sphere theorem Harmonic coordinate Harmonic radius 

Mathematics Subject Classification (2000)

53C20 53C23 53C24 


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Copyright information

© Springer Science+Business Media B.V. 2007

Authors and Affiliations

  1. 1.School of Mathematical SciencesQufu Normal UniversityQufuChina
  2. 2.Department of MathematicsEast China Normal UniversityShanghaiChina

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