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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 M. Gerstenhaber and 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 (quasi-)conformal mappings, variational methods
30F45Conformal metrics (hyperbolic, Poincaré, distance functions)
30F60Teichmüller theory