Two-dimensional Geometric Variational Problems - Tapa blanda

Sinopsis

This monograph addresses variational problems for mappings from a surface equipped with a conformal structure into Euclidean space or a Riemannian manifold. It is assumed that the variational problems are invariant under conformal reparametrizations of the domain. Solutions to such variational problems consist of conformal mappings between surfaces, minimal surfaces in Riemannian manifolds, harmonic maps from a surface into a Riemannian manifold, and solutions of prescribed mean curvature equations. A general theory of such variational problems is presented, proving existence and regularity theorems with particular conceptual emphasis on the geometric aspects of the theory and thoroughly investigating the connections with complex analysis. The approach is purely parametric, and consequently, does not address the question of geometric regularity of the solutions (immersion and embeddedness properties).

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