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Hausdorff dimension of escaping sets of meromorphic functions

Aspenberg, Magnus LU and Cui, Weiwei LU (2021) In Transactions of the American Mathematical Society 374(9). p.6145-6178
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.

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author
and
organization
publishing date
type
Contribution to journal
publication status
published
subject
in
Transactions of the American Mathematical Society
volume
374
issue
9
pages
34 pages
publisher
American Mathematical Society (AMS)
external identifiers
  • scopus:85113318593
ISSN
0002-9947
DOI
10.1090/tran/8299
language
English
LU publication?
yes
id
23168b3f-800a-4de2-ae3e-2d7812a7d8e6
date added to LUP
2022-02-04 16:12:19
date last changed
2022-04-21 22:53:55
@article{23168b3f-800a-4de2-ae3e-2d7812a7d8e6,
  abstract     = {{<p>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.</p>}},
  author       = {{Aspenberg, Magnus and Cui, Weiwei}},
  issn         = {{0002-9947}},
  language     = {{eng}},
  number       = {{9}},
  pages        = {{6145--6178}},
  publisher    = {{American Mathematical Society (AMS)}},
  series       = {{Transactions of the American Mathematical Society}},
  title        = {{Hausdorff dimension of escaping sets of meromorphic functions}},
  url          = {{http://dx.doi.org/10.1090/tran/8299}},
  doi          = {{10.1090/tran/8299}},
  volume       = {{374}},
  year         = {{2021}},
}