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Convex functions on Alexandrov surfaces
Author(s):
Yukihiro
Mashiko
Journal:
Trans. Amer. Math. Soc.
351
(1999),
3549-3567.
MSC (1991):
Primary 53C20
Posted:
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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Additional Information:
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:
10.1090/S0002-9947-99-02193-5
PII:
S 0002-9947(99)02193-5
Keywords:
Alexandrov spaces of curvature bounded below,
convex functions
Received by editor(s):
April 10, 1997
Posted:
February 5, 1999
Copyright of article:
Copyright
1999,
American Mathematical Society
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