Capacity and Equilibrium Energy of Condensers (April 2021)
In this lecture, Dr. Stamatis Pouliasis from Texas Tech, USA, will introduce the basic notions of condensers in Euclidean spaces, such as capacity, energy, equilibrium measure and potential, and will describe their basic properties. In particular, three equivalent approaches based on the Dirichlet integral, the Green function, and the discrete energy will be presented.
The lecture will also consider a variation of the positive plate of a condenser, described via a family of smooth domains whose boundaries are level sets of a smooth function V. It will be shown that, if V is subharmonic, then the energy of the condenser is a concave function of the parameter, and the cases where this function is affine will be characterized.
For more information, please contact [email protected].
