TY - JOUR

T1 - Stability of strongly Lipschitz contractible balls in Alexandrov spaces

AU - Mitsuishi, Ayato

AU - Yamaguchi, Takao

PY - 2014

Y1 - 2014

N2 - Recently, we proved that every finite dimensional Alexandrov space is strongly locally Lipschitz contractible. In the present paper, we consider the set M of all isometry classes of Alexandrov spaces of curvature≥ –1 and of fixed dimension having upper diameter bound and lower volume bound, and prove that there exists a constant N depending on the parameters determining M such that every space in M can be covered by at most N strongly Lipschitz contractible balls. Also, we prove that there exists a constant N′ depending on M such that every space in M can be covered by at most N′ strongly Lipschitz contractible and convex regions.

AB - Recently, we proved that every finite dimensional Alexandrov space is strongly locally Lipschitz contractible. In the present paper, we consider the set M of all isometry classes of Alexandrov spaces of curvature≥ –1 and of fixed dimension having upper diameter bound and lower volume bound, and prove that there exists a constant N depending on the parameters determining M such that every space in M can be covered by at most N strongly Lipschitz contractible balls. Also, we prove that there exists a constant N′ depending on M such that every space in M can be covered by at most N′ strongly Lipschitz contractible and convex regions.

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U2 - 10.1007/s00209-014-1289-3

DO - 10.1007/s00209-014-1289-3

M3 - Article

VL - 277

SP - 995

EP - 1009

JO - Mathematische Zeitschrift

JF - Mathematische Zeitschrift

SN - 0025-5874

IS - 3-4

ER -