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Heat-flow methods for harmonic maps of surfaces and applications to free boundary problems. (English) Zbl 0651.53045
Partial differential equations, Proc. Lat. Am. Sch. Math., ELAM-8, Rio de Janeiro/Braz. 1986, Lect. Notes Math. 1324, 293-319 (1988).
[For the entire collection see Zbl 0641.00012.]
Author’s summary: “In Comment. Math. Helv. 60, 558-581 (1985; Zbl 0595.58013), the author extended the Eells-Sampson method for constructing harmonic maps between manifolds to maps from a surface to an arbitrary compact manifold. We review the results in [loc. cit.] and present several applications: First a new proof of the Sacks-Uhlenbeck results is given. Then we study minimal surfaces and surfaces of constant mean curvature with free boundaries on a supporting surface in \({\mathbb{R}}^ 3.\)”
Reviewer: J.Eells

MSC:
53C42 Differential geometry of immersions (minimal, prescribed curvature, tight, etc.)
58E20 Harmonic maps, etc.
53A10 Minimal surfaces in differential geometry, surfaces with prescribed mean curvature