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- W4287634872 abstract "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 Karcher's classical volume comparison theorem. Our main tool is the gradient flow of semi-concave functions." @default.
- W4287634872 created "2022-07-25" @default.
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- W4287634872 date "2020-10-22" @default.
- W4287634872 modified "2023-09-23" @default.
- W4287634872 title "Volume estimates for Alexandrov Spaces with convex boundaries" @default.
- W4287634872 hasPublicationYear "2020" @default.
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