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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Convex functions on Alexandrov surfaces


Author: Yukihiro Mashiko
Journal: Trans. Amer. Math. Soc. 351 (1999), 3549-3567
MSC (1991): Primary 53C20
DOI: https://doi.org/10.1090/S0002-9947-99-02193-5
Published electronically: February 5, 1999
MathSciNet review: 1473452
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Abstract: We investigate the topological structure of Alexandrov surfaces of curvature bounded below which possess convex functions. We do not assume the continuities of these functions. Nevertheless, if the convex functions satisfy a condition of local nonconstancy, then the topological structures of Alexandrov surfaces and the level sets configurations of these functions in question are determined.


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Yukihiro Mashiko
Affiliation: Graduate School of Mathematics, Kyushu University, 6-10-1 Hakozaki, Higashi-ku, Fukuoka, 812-81 Japan
Email: mashiko@math.kyushu-u.ac.jp

DOI: https://doi.org/10.1090/S0002-9947-99-02193-5
Keywords: Alexandrov spaces of curvature bounded below, convex functions
Received by editor(s): April 10, 1997
Published electronically: February 5, 1999
Article copyright: © Copyright 1999 American Mathematical Society