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2017 Real analytic complete non-compact surfaces in Euclidean space with finite total curvature arising as solutions to ODEs
Peter Gilkey, Chan Yong Kim, JeongHyeong Park
Tohoku Math. J. (2) 69(1): 1-23 (2017). DOI: 10.2748/tmj/1493172124

Abstract

We use the solution space of a pair of ODEs of at least second order to construct a smooth surface in Euclidean space. We describe when this surface is a proper embedding which is geodesically complete with finite total Gauss curvature. If the associated roots of the ODEs are real and distinct, we give a universal upper bound for the total Gauss curvature of the surface which depends only on the orders of the ODEs and we show that the total Gauss curvature of the surface vanishes if the ODEs are second order. We examine when the surfaces are asymptotically minimal.

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Peter Gilkey. Chan Yong Kim. JeongHyeong Park. "Real analytic complete non-compact surfaces in Euclidean space with finite total curvature arising as solutions to ODEs." Tohoku Math. J. (2) 69 (1) 1 - 23, 2017. https://doi.org/10.2748/tmj/1493172124

Information

Published: 2017
First available in Project Euclid: 26 April 2017

zbMATH: 1368.53002
MathSciNet: MR3640010
Digital Object Identifier: 10.2748/tmj/1493172124

Subjects:
Primary: 53A05
Secondary: 53C21

Rights: Copyright © 2017 Tohoku University

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Vol.69 • No. 1 • 2017
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