4 papers
A note on the squeezing function
Alexander Yu. Solynin
The squeezing problem on can be stated as follows. Suppose that is a multiply connected domain in the unit disk containing the origin . How far c…
Infinitesimally small spheres and conformally invariant metrics
Stamatis Pouliasis, Alexander Yu. Solynin
The modulus metric (also called the capacity metric) on a domain can be defined as $μ_D(x,y)=\inf\{\mbox{cap}\,(D,γ)\}$, where ${\mbox{cap}}\,(D,γ)$ stands…
Continuous symmetrization via polarization
Alexander Yu. Solynin
We discuss a one-parameter family of transformations which changes sets and functions continuously into their (k,n)-Steiner symmetrizations. Our construction consists of two stages…
An isoperimetric inequality for logarithmic capacity of polygons
Alexander Yu. Solynin, Victor A Zalgaller
We verify an old conjecture of G. Polya and G. Szego saying that the regular n-gon minimizes the logarithmic capacity among all n-gons with a fixed area.