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MiS Preprint
78/2009

The regularity of harmonic maps into spheres and applications to Bernstein problems

Jürgen Jost, Yuanlong Xin and Ling Yang

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 quasi-linear 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.

Received:
14.12.2009
Published:
14.12.2009
MSC Codes:
58E20, 53A10

Related publications

inJournal
2012 Repository Open Access
Jürgen Jost, Yuan-Long Xin and Ling Yang

The regularity of harmonic maps into spheres and applications to Bernstein problems

In: Journal of differential geometry, 90 (2012) 1, pp. 131-176