The metric measure boundary of spaces with Ricci curvature bounded below

被引：2
|
作者：
Brue, Elia [1 ]
Mondino, Andrea [2 ]
Semola, Daniele [2 ]
机构：
[1] Inst Adv Study, Sch Math, 1 Einstein Dr, Princeton, NJ 05840 USA
[2] Univ Oxford, Math Inst, Oxford OX2 6GG, England
来源：
GEOMETRIC AND FUNCTIONAL ANALYSIS | 2023年 / 33卷 / 03期
基金：
欧洲研究理事会;
关键词：
DIMENSION CONDITION; LOCAL POINCARE; ALEXANDROV; EQUIVALENCE; MANIFOLDS; RIGIDITY; GEOMETRY;
D O I：
10.1007/s00039-023-00626-x
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We solve a conjecture raised by Kapovitch, Lytchak and Petrunin in [KLP21] by showing that the metric measure boundary is vanishing on any RCD(K, N) space (X, d, 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.
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页码：593 / 636
页数：44
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