The asymptotic behavior of modulus of Grötsch’s and Teichmüller’s rings in the space of a very large dimension

In the geometric theory of functions, especially in the theory of spatial quasi-conformal mappings, the role of a very useful tool play Grötsch’s and Teichmüller’s rings (capacitors or condensers). We will discuss several open problems of the theory which stimulate the research of the asymptotic behavior of the conformal capacity of Grötsch’s and Teichmüller’s capacitors on the growing dimension of the space, and we will describe this asymptotic behavior.