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Variational problem of some quadratic functionals in complex analysis. (English) Zbl 0945.30023
For maps between marked closed Riemann surfaces a program of H. E. Rauch (see {\it M. Gerstenhaber} and {\it H. E. Rauch}, Proc. Natl. Acad. Sci. 40, 808-812, 991-994 (1954; Zbl 0056.07502) studied the existence of Teichmüller’s extremal map by minimizing the energy functionals. The paper under review contributes to that program, by examining related quadratic functionals of maps.

30C70Extremal problems for conformal and quasiconformal mappings, variational methods
30F45Conformal metrics (hyperbolic, Poincaré, distance functions)
30F60Teichmüller theory
Full Text: DOI
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