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math.CV2021
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…
math.CV2018
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…
math.CV2005
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.