The metric measure boundary of spaces with Ricci curvature bounded below

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 o...

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Bibliographic Details
Published in:Geometric and functional analysis 2023-06, Vol.33 (3), p.593-636
Main Authors: Bruè, Elia, Mondino, Andrea, Semola, Daniele
Format: Article
Language:English
Subjects:
Analysis
Geodesy
Mathematics
Mathematics and Statistics
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Summary: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.
ISSN:1016-443X
1420-8970
DOI:10.1007/s00039-023-00626-x