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October 2020 Limiting behavior of sequences of properly embedded minimal disks
David Hoffman, Brian White
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J. Differential Geom. 116(2): 281-319 (October 2020). DOI: 10.4310/jdg/1603936813

Abstract

We develop a theory of “minimal $\theta$-graphs” and characterize the behavior of limit laminations of such surfaces, including an understanding of their limit leaves and their curvature blow-up sets. We use this to prove that it is possible to realize families of catenoids in euclidean space as limit leaves of sequences of embedded minimal disks, even when there is no curvature blow-up. Our methods work in a more general Riemannian setting, including hyperbolic space. This allows us to establish the existence of a complete, simply connected, minimal surface in hyperbolic space that is not properly embedded.

Funding Statement

This work was partially supported by grants to Brian White from the Simons Foundation (#396369) and from the National Science Foundation (DMS 1404282).

Citation

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David Hoffman. Brian White. "Limiting behavior of sequences of properly embedded minimal disks." J. Differential Geom. 116 (2) 281 - 319, October 2020. https://doi.org/10.4310/jdg/1603936813

Information

Received: 1 July 2017; Published: October 2020
First available in Project Euclid: 29 October 2020

zbMATH: 07269226
MathSciNet: MR4168205
Digital Object Identifier: 10.4310/jdg/1603936813

Rights: Copyright © 2020 Lehigh University

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Vol.116 • No. 2 • October 2020
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