Lower bounds for areas of images of discs
Ruslan Salimov, Bogdan Klishchuk
TL;DR
This paper establishes lower bounds for the areas of images of discs under Q-homeomorphisms with respect to the p-modulus on the complex plane, providing solutions to extremal problems related to area minimization.
Contribution
It introduces new lower area estimates for images of discs under Q-homeomorphisms and solves the extremal problem of minimizing the area functional of these images.
Findings
Derived lower bounds for areas of images of discs
Solved extremal problem for area minimization
Provided theoretical framework for Q-homeomorphisms with p>2
Abstract
In this article we consider Q-homeomorphisms with respect to the p-modulus on the complex plane with p>2. It is obtained a lower area estimate for image of discs under such mappings. We solved the extremal problem about minimization of the area functional of images of discs.
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Taxonomy
TopicsAnalytic and geometric function theory · Differential Equations and Boundary Problems