论文标题
具有凸边界的Alexandrov空间的体积估算值
Volume estimates for Alexandrov Spaces with convex boundaries
论文作者
论文摘要
在本说明中，我们估算了闭合或非弯曲的Alexandrov空间$ x $的上限，并严格凸出边界。我们还讨论了平等案例。特别是，当达到体积上限时，边界猜想就会存在。我们的定理也可以应用于具有非平滑边界的Riemannian歧管，该歧管概括了Heintze和Karcher的经典体积比较定理。我们的主要工具是半圆柱函数的梯度流。
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.
