Lower bounds for the volume of the image of a ball - Klishchuk, Bogdan; Salimov, Ruslan (Ukrains’kyi Matematychnyi Zhurnal, 2023)
We consider ring $Q$-homeomorphisms with respect to $p$-modulus in the space $\Bbb R^{n}$ as $p>n$. We obtain a lower bound for thevolume of the image of a ball under such mappings. We solve the extremal problems on minimizing of the functionals of the volume ofthe image of a ball and the area of the image of a sphere.