ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

8. Analysis

1991 MS Classification: 30 Vo Dang Thao, University of Ho Chi Minh City, Vietnam Area Problem for quasiconformal mappings Let A be an n-multiply connected domain of the extended complex plane containing 0 and z_{1}. Let F be the class of K-quasiconformal mappings w = f(z) of A satisfying f(0) = 0, arg f(z_{1}) = 0 and, where s(r) is the area of the image of the disk |z| < r under the mapping f. Denote by S(f), f ∈ F, the area of f(A). The problem now consists in finding all the particular functions f_{0} ∈ F satisfying S(f)S(f_{0}), f ∈ F. It is showed that any extremal domain f_{0}(A) must be a disk |w| < R with n − 1 concentric circular slits and the largest number of extremal functions may be n. Reference: V. D. Thao, Quelques inégalités d’aires pour les représentations quasi-conformes, Rev. Roumaine Math. Pures Appl. 36 (1991), 9-10, 521-