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2018 Min–max for phase transitions and the existence of embedded minimal hypersurfaces
Marco A. M. Guaraco
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J. Differential Geom. 108(1): 91-133 (2018). DOI: 10.4310/jdg/1513998031

Abstract

Strong parallels can be drawn between the theory of minimal hypersurfaces and the theory of phase transitions. Borrowing ideas from the former we extend recent results on the regularity of stable phase transition interfaces to the finite Morse index case. As an application we present a PDE-based proof of the celebrated theorem of Almgren–Pitts, on the existence of embedded minimal hypersurfaces in compact manifolds. We compare our results with other min–max theories.

Funding Statement

The author was partly supported by CAPES-Brazil and NSF Grant DMS-1104592.

Citation

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Marco A. M. Guaraco. "Min–max for phase transitions and the existence of embedded minimal hypersurfaces." J. Differential Geom. 108 (1) 91 - 133, 2018. https://doi.org/10.4310/jdg/1513998031

Information

Received: 13 August 2015; Published: 2018
First available in Project Euclid: 23 December 2017

zbMATH: 06846975
MathSciNet: MR3743704
Digital Object Identifier: 10.4310/jdg/1513998031

Rights: Copyright © 2018 Lehigh University

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Vol.108 • No. 1 • 2018
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