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Volume estimates for Alexandrov Spaces with convex boundaries

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 نشر من قبل Jian Ge
 تاريخ النشر 2020
  مجال البحث
والبحث باللغة English
 تأليف Jian Ge




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In this note, we estimate the upper bound of volume of closed positively or nonnegatively curved Alexandrov space $X$ with strictly convex boundary. We also discuss the equality case. In particular, the Boundary Conjecture holds when the volume upper bound is achieved. Our theorem also can be applied to Riemannian manifolds with non-smooth boundary, which generalizes Heintze and Karchers classical volume comparison theorem. Our main tool is the gradient flow of semi-concave functions.



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