2003/12/11 by Wenyi Chen, Chen, Wenyi, Juergen Jost +1
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Geometric Analysis and Curvature Flows #Nonlinear Partial Differential Equations #math.AP #math.DG #msc:58E20
paper · pdf · doi:10.48550/arxiv.math/0312233
To appear in Comm.Anal.Geom
arxiv created 2003/12/11 · arxiv updated 2009/12/01
We consider maps into Riemannian manifolds of non-positive curvature and start developing a systematic PDE theory. We control the Sobolev H2,2-norm of such a map in terms of its energy, the L2-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.