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).
- ISBN10 0471928399
- ISBN13 9780471928393
- Publish Date 23 January 1991
- Publish Status Out of Print
- Out of Print 14 January 1999
- Publish Country GB
- Publisher John Wiley and Sons Ltd
- Imprint John Wiley & Sons Ltd
- Format Hardcover
- Pages 250
- Language English