Surveys in Differential Geometry

Volume 19 (2014)

Regularity of stable minimal hypersurfaces: Recent advances in the theory and applications

Pages: 231 – 301

DOI: https://dx.doi.org/10.4310/SDG.2014.v19.n1.a9

Author

Neshan Wickramasekera (Department of Pure Mathematics and Mathematical Statistics (DPMMS), Centre for Mathematical Sciences, University of Cambridge, United Kingdom)

Abstract

We survey some recent progress in the regularity theory of stable minimal hypersurfaces, describing also earlier work related to the recent results, some applications of the recent results, and key aspects of their proofs.

Keywords

varifolds, currents, stable minimal hypersurfaces, first variation, second variation, stationarity, stability, tangent cones, regularity theory, classical singularities, branch points, maximum principle, unique continuation, phase transition, blow up

2010 Mathematics Subject Classification

35-xx, 53-xx

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Published 6 March 2015