Convex functions on Alexandrov surfaces
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- by Yukihiro Mashiko
- Trans. Amer. Math. Soc. 351 (1999), 3549-3567
- DOI: https://doi.org/10.1090/S0002-9947-99-02193-5
- Published electronically: February 5, 1999
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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.References
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Bibliographic 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
- Received by editor(s): April 10, 1997
- Published electronically: February 5, 1999
- © Copyright 1999 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 351 (1999), 3549-3567
- MSC (1991): Primary 53C20
- DOI: https://doi.org/10.1090/S0002-9947-99-02193-5
- MathSciNet review: 1473452