Séminaire d'Analyse

On Squeezing Function for Planar Domains

by Yekta Okten (IMT)

Salle Pellos (1R2-207)

Salle Pellos (1R2-207)


The squeezing function is a biholomorphic invariant defined on domains in $\mathbb C^n$ which arose from the study of invariant metrics on Teichmüller spaces of Riemann surfaces. Roughly speaking, it measures how much a domain looks like the unit ball looking at a fixed point. The behaviour of the squeezing function is well studied however very few non-trivial explicit formulas of squeezing functions have been found. In this talk, with an elementary technique we will establish the explicit formulas of squeezing functions on doubly connected planar domains and provide bounds to squeezing functions of higher connected domains. In conclusion, we will mention further questions about explicit formulas of squeezing functions and canonical conformal maps.