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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.
MSC:
30C70Extremal problems for (quasi-)conformal mappings, variational methods
30F45Conformal metrics (hyperbolic, Poincaré, distance functions)
30F60Teichmüller theory