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July, 2015 Global existence of generalized rotational hypersurfaces with prescribed mean curvature in Euclidean spaces, I
Katsuei KENMOTSU, Takeyuki NAGASAWA
J. Math. Soc. Japan 67(3): 1077-1108 (July, 2015). DOI: 10.2969/jmsj/06731077

Abstract

We prove that for a given continuous function $H(s)$, $(-\infty$ < $s$ < $\infty)$, there exists a globally defined generating curve of a rotational hypersurface in a Euclidean space such that the mean curvature is $H(s)$. We also prove a similar theorem for generalized rotational hypersurfaces of $O(l+1)\times O(m+1)$-type. The key lemmas in this paper show the existence of solutions for singular initial value problems of ordinary differential equations satisfied using generating curves of those hypersurfaces.

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Katsuei KENMOTSU. Takeyuki NAGASAWA. "Global existence of generalized rotational hypersurfaces with prescribed mean curvature in Euclidean spaces, I." J. Math. Soc. Japan 67 (3) 1077 - 1108, July, 2015. https://doi.org/10.2969/jmsj/06731077

Information

Published: July, 2015
First available in Project Euclid: 5 August 2015

zbMATH: 1325.53017
MathSciNet: MR3376579
Digital Object Identifier: 10.2969/jmsj/06731077

Subjects:
Primary: 53C42
Secondary: 34A12

Keywords: generalized rotational hypersurfaces , mean curvature

Rights: Copyright © 2015 Mathematical Society of Japan

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Vol.67 • No. 3 • July, 2015
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