Intrinsic semiharmonic maps

Reference:

Moser, R., 2011. Intrinsic semiharmonic maps. Journal of Geometric Analysis, 21 (3), pp. 588-598.

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Official URL:

http://dx.doi.org/10.1007/s12220-010-9159-7

Abstract

For maps from a domain $\Omega \subset \mathbb{R}^m$ into a Riemannian manifold $N$, a functional coming from the norm of a fractional Sobolev space has recently been studied by Da Lio and Rivière. An intrinsically defined functional with a similar behavior also exists, and its first variation can be identified with a Dirichlet-to-Neumann map belonging to the harmonic map problem. The critical points have regularity properties analogous to harmonic maps.

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