Sınırlı kümelerde değişmez metrikler ve sıkıştırma fonksiyonları

In this thesis we will study the biholomorphically invariant objects called squeezing functions. They are closely releated to invariant metrics on bounded domains and describe how much a domain looks like the unit ball looking on a fixed point. In the main part of this thesis, we will give our results on squeezing functions on planar domains. In particular, our main result provides an alternative proof for the explicit formulas of squeezing functions on annuli. Also, we survey results on boundary behaviour of squeezing functions.