A splitting theorem for infinite dimensional Alexandrov spaces with nonnegative curvature and its applications

Ayato Mitsuishi

doi:10.1007/s10711-009-9390-1

A splitting theorem for infinite dimensional Alexandrov spaces with nonnegative curvature and its applications

Ayato Mitsuishi

SCI - Mathematics

Research output: Contribution to journal › Article › peer-review

8 Citations (Scopus)

Abstract

We prove a splitting theorem for Alexandrov space of nonnegative curvature without properness assumption. As a corollary, we obtain a maximal radius theorem for Alexandrov spaces of curvature bounded from below by 1 without properness assumption. Also, we provide new examples of infinite dimensional Alexandrov spaces of nonnegative curvature.

Original language	English
Pages (from-to)	101-114
Number of pages	14
Journal	Geometriae Dedicata
Volume	144
Issue number	1
DOIs	https://doi.org/10.1007/s10711-009-9390-1
Publication status	Published - 2010 Jan

Keywords

Alexandrov space
Infinite dimension
Lower curvature bound
Maximal radius sphere theorem
Splitting theorem

ASJC Scopus subject areas

Geometry and Topology

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10.1007/s10711-009-9390-1

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abstract = "We prove a splitting theorem for Alexandrov space of nonnegative curvature without properness assumption. As a corollary, we obtain a maximal radius theorem for Alexandrov spaces of curvature bounded from below by 1 without properness assumption. Also, we provide new examples of infinite dimensional Alexandrov spaces of nonnegative curvature.",

keywords = "Alexandrov space, Infinite dimension, Lower curvature bound, Maximal radius sphere theorem, Splitting theorem",

author = "Ayato Mitsuishi",

note = "Funding Information: Acknowledgments The author would like to express his thanks to Professor Takao Yamaguchi for his suggestions, encouragement, and comments. Also the author would like to thank Takumi Yokota for his suggestions and comments. This work was partially supported by Research Fellowships of the Japan Society for the Promotion of Science for Young Scientists.",

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N2 - We prove a splitting theorem for Alexandrov space of nonnegative curvature without properness assumption. As a corollary, we obtain a maximal radius theorem for Alexandrov spaces of curvature bounded from below by 1 without properness assumption. Also, we provide new examples of infinite dimensional Alexandrov spaces of nonnegative curvature.

AB - We prove a splitting theorem for Alexandrov space of nonnegative curvature without properness assumption. As a corollary, we obtain a maximal radius theorem for Alexandrov spaces of curvature bounded from below by 1 without properness assumption. Also, we provide new examples of infinite dimensional Alexandrov spaces of nonnegative curvature.

KW - Alexandrov space

KW - Infinite dimension

KW - Lower curvature bound

KW - Maximal radius sphere theorem

KW - Splitting theorem

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A splitting theorem for infinite dimensional Alexandrov spaces with nonnegative curvature and its applications

Abstract

Keywords

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