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Graphs with constant ratio of mean curvatures and spherical caps

Published online by Cambridge University Press:  17 April 2009

Sung-Eun Koh
Sung-Eun Koh
Affiliation:
Department of Mathematics, Konkuk University, Seoul, 143-701Korea, e-mail: sekoh@konkuk.ac.kr
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Let f be a smooth nonconstant function defined on an n dimensional ball and zero on the boundary n − 1 dimensional sphere. It is shown that the graph of f is a spherical cap (1) if f is positive and if the ratio Hk/Hr is a nonzero constant for 1 ≤ k < r ≤ n on the graph of f or (2) if the ratio Hn/Hk is a nonzero constant on the graph of f.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 74 , Issue 1 , August 2006 , pp. 1 - 5
Copyright
Copyright © Australian Mathematical Society 2006

References

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