论文标题
RICCI曲率界限的空间的度量测量边界
The metric measure boundary of spaces with Ricci curvature bounded below
论文作者
论文摘要
我们通过表明公制测量边界在任何$ {\ rm rcd}（k，n）$空间上消失了，我们解决了由卡波维奇，莱特查克和彼得鲁宁提出的猜想。我们的结果与[Kapovitch-Lytchak-Petrunin '21]结合在一起，解决了一个公开的问题，即1996年，Perelman和Petrunin在Alexandrov空间上存在无限的大地测量空间。
We solve a conjecture raised by Kapovitch, Lytchak, and Petrunin by showing that the metric measure boundary is vanishing on any ${\rm RCD}(K,N)$ space without boundary. Our result, combined with [Kapovitch-Lytchak-Petrunin '21], settles an open question about the existence of infinite geodesics on Alexandrov spaces without boundary raised by Perelman and Petrunin in 1996.
