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August 2018 Explicit Björling Surfaces with Prescribed Geometry
Rafael López, Matthias Weber
Michigan Math. J. 67(3): 561-584 (August 2018). DOI: 10.1307/mmj/1531447375

Abstract

We develop a new method to construct explicit regular minimal surfaces in Euclidean space that are defined on the entire complex plane with controlled geometry. More precisely, we show that for a large class of planar curves (x(t),y(t)), we can find a third coordinate z(t) and normal fields n(t) along the space curve c(t)=(x(t),y(t),z(t)) so that the Björling formula applied to c(t) and n(t) can be explicitly evaluated. We give many examples.

Citation

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Rafael López. Matthias Weber. "Explicit Björling Surfaces with Prescribed Geometry." Michigan Math. J. 67 (3) 561 - 584, August 2018. https://doi.org/10.1307/mmj/1531447375

Information

Received: 31 October 2016; Revised: 11 May 2017; Published: August 2018
First available in Project Euclid: 13 July 2018

zbMATH: 06969984
MathSciNet: MR3835564
Digital Object Identifier: 10.1307/mmj/1531447375

Subjects:
Primary: 53A10, 53C43
Secondary: 53C45

Rights: Copyright © 2018 The University of Michigan

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Vol.67 • No. 3 • August 2018
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