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The metric measure boundary of spaces with Ricci curvature bounded below
Geometric and Functional Analysis ( IF 2.4 ) Pub Date : 2023-04-20 , DOI: 10.1007/s00039-023-00626-x Elia Bruè , Andrea Mondino , Daniele Semola
中文翻译:
度量测量具有以下界的里奇曲率的空间边界
更新日期:2023-04-20
Geometric and Functional Analysis ( IF 2.4 ) Pub Date : 2023-04-20 , DOI: 10.1007/s00039-023-00626-x Elia Bruè , Andrea Mondino , Daniele Semola
We solve a conjecture raised by Kapovitch, Lytchak and Petrunin in [KLP21] by showing that the metric measure boundary is vanishing on any \({{\,\textrm{RCD}\,}}(K,N)\) space \((X,{\textsf{d}},{\mathscr {H}}^N)\) without boundary. Our result, combined with [KLP21], settles an open question about the existence of infinite geodesics on Alexandrov spaces without boundary raised by Perelman and Petrunin in 1996.
中文翻译:
![](https://scdn.x-mol.com/jcss/images/paperTranslation.png)
度量测量具有以下界的里奇曲率的空间边界
我们通过证明度量测度边界在任何\ ({{\,\textrm{RCD}\,}}(K,N)\)空间上消失来解决 Kapovitch、Lytchak 和 Petrunin 在 [KLP21] 中提出的猜想((X,{\textsf{d}},{\mathscr {H}}^N)\)无边界。我们的结果与 [KLP21] 相结合,解决了 Perelman 和 Petrunin 在 1996 年提出的关于无边界 Alexandrov 空间上是否存在无限测地线的悬而未决的问题。