论文标题
在具有较低曲率边界的公制测量空间的固有和外在边界上
On the intrinsic and extrinsic boundary for metric measure spaces with lower curvature bounds
论文作者
论文摘要
我们表明，如果Alexandrov space $ x $具有与$ x $边界相同的尺寸分离的Alexandrov子空间$ \ bar的barω$，则$ \ barω$的拓扑边界与其Alexandrov Boundare的拓扑边界相吻合。同样，如果未汇合的RCD（k，n）空间$ x $具有非策略的RCD（k，n）子空间$ \ barω$与$ x $的边界的分离，并且具有轻度的边界条件，则具有$ \ barω$ $ conciides的拓扑边界与菲利普斯·菲利普斯·基吉利（Deippis-Gigli）边界。然后，我们讨论有关这种等价类型的凸性的一些后果。
We show that if an Alexandrov space $X$ has an Alexandrov subspace $\bar Ω$ of the same dimension disjoint from the boundary of $X$, then the topological boundary of $\bar Ω$ coincides with its Alexandrov boundary. Similarly, if a noncollapsed RCD(K,N) space $X$ has a noncollapsed RCD(K,N) subspace $\bar Ω$ disjoint from boundary of $X$ and with mild boundary condition, then the topological boundary of $\bar Ω$ coincides with its De Philippis-Gigli boundary. We then discuss some consequences about convexity of such type of equivalence.
