Geodesic
A extremal problem for the areas of images of disks
Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 45, Tome 456 (2017), pp. 160-171

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We study metric properties of the ring $Q$-homeomorphisms with respect to the $p$-modulus, $p>2$, in the complex plane and establish lower bounds for the areas of disks. The extremal problem concerning minimization of the area functional is also solved. 
@article{ZNSL_2017_456_a13,
     author = {R. R. Salimov and B. A. Klishchuk},
     title = {A extremal problem for the areas of images of disks},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {160--171},
     publisher = {mathdoc},
     volume = {456},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2017_456_a13/}
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R. R. Salimov; B. A. Klishchuk. A extremal problem for the areas of images of disks. Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 45, Tome 456 (2017), pp. 160-171. http://geodesic.mathdoc.fr/item/ZNSL_2017_456_a13/