Squeezing functions of n-connected domains

Date

2024-8-2

Author

Can, Aslı

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The explicit formula of the squeezing function for the annulus firstly was given by Ng, Tang and Tsai (2021). In the paper of them, they used Loewner differential equations to prove the explicit formula. Later, Gumenyuk and Roth (2021) gave an alternative proof via potential theoretical tools. Their proof is easier to follow and much shorter. Additionally, they expand this proof by finding the way to identify all extremal functions. In the same year, Solynin(2021) gave another proof using moduli of families of curves in an annulus. Recently, Ökten (2021,2023) proved the formula geometrically. In this thesis, we will consider the potential theoretic proof of a characterization of the squeezing function of two-connected domains which yields an explicit formula of the squeezing function of the annulus.

Subject Keywords

Squeezing Function, Potential Theory, Subharmonic Functions

URI

https://hdl.handle.net/11511/110599

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Graduate School of Natural and Applied Sciences, Thesis