Tohoku Mathematical Journal, Second Series
Online ISSN : 2186-585X
Print ISSN : 0040-8735
ISSN-L : 0040-8735
REAL ANALYTIC COMPLETE NON-COMPACT SURFACES IN EUCLIDEAN SPACE WITH FINITE TOTAL CURVATURE ARISING AS SOLUTIONS TO ODES
Peter V. GilkeyChan Yong KimJeongHyeong Park
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2017 Volume 69 Issue 1 Pages 1-23

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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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