Hausdorff dimension of escaping sets of meromorphic functions

Magnus Aspenberg, Weiwei Cui

Research output: Contribution to journalArticlepeer-review

Abstract

We give a complete description of the possible Hausdorff dimensions of escaping sets for meromorphic functions with a finite number of singular values. More precisely, for any given d ϵ [0, 2] we show that there exists such a meromorphic function for which the Hausdorff dimension of the escaping set is equal to d. The main ingredient is to glue together suitable meromorphic functions by using quasiconformal mappings. Moreover, we show that there are uncountably many quasiconformally equivalent meromorphic functions for which the escaping sets have different Hausdorff dimensions.

Original languageEnglish
Pages (from-to)6145-6178
Number of pages34
JournalTransactions of the American Mathematical Society
Volume374
Issue number9
DOIs
Publication statusPublished - 2021

Subject classification (UKÄ)

  • Mathematical Analysis

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