Complementary isoperimetric inequalities for capacity, polarization, and virtual mass

Abstract

This paper deals with isoperimetric inequalities for polarization, virtual mass and capacity of a body B in R³. The first part of the paper is restricted to certain symmetric regions for which the above mentioned problems may be interpreted as electrostatic problems in R⁵. This makes it possible to use Brunn-Minkowski type concavity properties for the electrostatic capacity established recently by C. Borell in [3]. In the second part of the paper we construct lower and upper bounds for polarization and virtual mass based on two identities obtained recently in [12] and valid for starshaped regions B

Keywords:

• Inequalities
• capacity
• polarization
• virtual mass

AMS(MOS)::

• 35J05
• 35J25