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Main Title: Discrete constant mean curvature surfaces and their index
Author(s): Polthier, Konrad
Rossman, Wayne
Type: Article
Language Code: en
Abstract: We define triangulated piecewise linear constant mean curvature surfaces using a variational characterization. These surfaces are critical for area amongst continuous piecewise linear variations which preserve the boundary conditions, the simplicial structures, and (in the nonminimal case) the volume to one side of the surfaces. We then find explicit formulas for complete examples, such as discrete minimal catenoids and helicoids. We use these discrete surfaces to study the index of unstable minimal surfaces, by numerically evaluating the spectra of their Jacobi operators. Our numerical estimates confirm known results on the index of some smooth minimal surfaces, and provide additional information regarding their area-reducing variations. The approach here deviates from other numerical investigations in that we add geometric interpretation to the discrete surfaces.
Issue Date: 2002
Date Available: 2-Oct-2018
DDC Class: 510 Mathematik
Subject(s): curvature surface
Jacobi operators
geometric interpretation
Journal Title: Journal für die reine und angewandte Mathematik
Publisher: De Gruyter
Publisher Place: Berlin
Volume: 2002
Issue: 549
Publisher DOI: 10.1515/crll.2002.066
Page Start: 47
Page End: 77
EISSN: 1435-5345
ISSN: 0075-4102
Notes: Dieser Beitrag ist mit Zustimmung des Rechteinhabers aufgrund einer (DFG geförderten) Allianz- bzw. Nationallizenz frei zugänglich.
This publication is with permission of the rights owner freely accessible due to an Alliance licence and a national licence (funded by the DFG, German Research Foundation) respectively.
Appears in Collections:Inst. Mathematik » Publications

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