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January 2012 The regularity of harmonic maps into spheres and applications to Bernsteing problems
Jűrgen Jost, Yuanlong Xin, Ling Yang
J. Differential Geom. 90(1): 131-176 (January 2012). DOI: 10.4310/jdg/1335209491

Abstract

We show the regularity of, and derive a-priori estimates for (weakly) harmonic maps from a Riemannian manifold into a Euclidean sphere under the assumption that the image avoids some neighborhood of a half-equator. The proofs combine constructions of strictly convex functions and the regularity theory of quasilinear elliptic systems.

We apply these results to the spherical and Euclidean Bernstein problems for minimal hypersurfaces, obtaining new conditions under which compact minimal hypersurfaces in spheres or complete minimal hypersurfaces in Euclidean spaces are trivial.

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Jűrgen Jost. Yuanlong Xin. Ling Yang. "The regularity of harmonic maps into spheres and applications to Bernsteing problems." J. Differential Geom. 90 (1) 131 - 176, January 2012. https://doi.org/10.4310/jdg/1335209491

Information

Published: January 2012
First available in Project Euclid: 23 April 2012

zbMATH: 1250.53061
MathSciNet: MR2891479
Digital Object Identifier: 10.4310/jdg/1335209491

Rights: Copyright © 2012 Lehigh University

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Vol.90 • No. 1 • January 2012
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