A finite quotient of join in Alexandrov geometry
Authors:
Xiaochun Rong and Yusheng Wang
Journal:
Trans. Amer. Math. Soc. 374 (2021), 1095-1124
MSC (2020):
Primary 53C20, 53C23, 53C24
DOI:
https://doi.org/10.1090/tran/8194
Published electronically:
November 18, 2020
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Abstract | References | Similar Articles | Additional Information
Abstract: Given two -dimensional Alexandrov spaces
of curvature
, the join of
and
is an
-dimensional Alexandrov space
of curvature
, which contains
as convex subsets such that their points are
apart. If a group acts isometrically on a join that preserves
, then the orbit space is called a quotient of join. We show that an
-dimensional Alexandrov space
with curvature
is isometric to a finite quotient of join, if
contains two compact convex subsets
without boundary such that
and
are at least
apart and
.
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Additional Information
Xiaochun Rong
Affiliation:
Department of Mathematics, Capital Normal University, Beijing, People’s Republic of China; and Department of Mathematics, Rutgers University, New Brunswick, New Jersey 08903
Email:
rong@math.rutgers.edu
Yusheng Wang
Affiliation:
School of Mathematical Sciences (and Lab. math. Com. Sys.), Beijing Normal University, Beijing, 100875 People’s Republic of China
Email:
wyusheng@bnu.edu.cn
DOI:
https://doi.org/10.1090/tran/8194
Received by editor(s):
November 17, 2018
Received by editor(s) in revised form:
May 5, 2020
Published electronically:
November 18, 2020
Additional Notes:
The first author was supported in part by NSFC 11821101, BNSF Z19003, and a research fund from Capital Normal University
The second author was supported in part by NFSC 11971057 and BNSF Z190003.
Yusheng Wang is the corresponding author
Article copyright:
© Copyright 2020
American Mathematical Society