Lower bounds for the volume of the image of a ball

  • Bogdan Klishchuk Institute of Mathematics of NAS of Ukraine
  • Ruslan Salimov

Abstract

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 the
volume of the image of a ball under such mappings. We solve the extremal problems on minimizing of the functionals of the volume of
the image of a ball and the area of the image of a sphere.

Published
19.07.2023
How to Cite
KlishchukB., and SalimovR. “Lower Bounds for the Volume of the Image of a Ball”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 71, no. 6, July 2023, pp. 774-85, https://umj.imath.kiev.ua/index.php/umj/article/view/775.
Section
Research articles