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Open AccessMathematics

Lower bounds for the area of the image of a circle

B. Klishchuk, R. Salimov

2017Ufa Mathematical Journal

DOI: 10.13108/2017-9-2-55

tlooto Summary

A 2017 study found lower bounds for the area of a circle's image under Q-homeomorphisms with p-modulus greater than 2.

Abstract

In the work we consider Q-homeomorphisms w.r.t p-modulus on the complex plane as p > 2. We obtain a lower bound for the area of the image of a circle under such mappings. We solve the extremal problem on minimizing the functional of the area of the image of a circle.

Citation format

KLISHCHUK, B.; SALIMOV, R. Lower bounds for the area of the image of a circle. Ufa Mathematical Journal, 2017, 9: 55–61.