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Maps with prescribed tension fields

Wenyi Chen·Juergen Jost
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Abstract

We consider maps into Riemannian manifolds of non-positive curvature and start developing a systematic PDE theory. We control the Sobolev $H^{2,2}$-norm of such a map in terms of its energy, the $L^2$-norm of its tension field and a topological term depending on the homotopy class. We also solve a Dirchlet problem without an underlying variational structure, as an extension of the topic of harmonic maps with potentials.

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Wenyi Chen, Juergen Jost. 2003-12-11. Maps with prescribed tension fields. https://arxiv.org/abs/math/0312233

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