S. L. Krushkal

Quasiconformal Deformations of Holomorphic Functions

This paper deals with holomorphic functions from Bergman spaces $B^p$ in the disk and provides the existence of deformations (variations) which do not increase the norm of functions and preserve some other prescribed properties. Admissible variations are constructed (for even integer $p \geq 2$) using special quasiconformal maps of the complex plane (in line with a new approach to variational problems for holomorphic functions in Banach spaces).