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Some examples of Baker domains

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Walter Bergweiler, Jian-Hua Zheng

Complex Variables · Submitted 6 Oct 2011

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim We construct entire functions with hyperbolic and simply parabolic Baker domains on which the functions are not univalent.

how it is stated · asserted 1.00 read the record →

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arXiv ID1110.1232 (version 1)
Pith IDRUFPOGEY, Pith's permanent record of this paper and its review
CitationJian-Hua Zheng, Walter Bergweiler. "Some examples of Baker domains." arXiv:1110.1232 (2011). https://pith.science/paper/RUFPOGEY
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The compiled record

The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

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Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 2,861 input tokens, $0.0001 reported.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.23 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.04 · compares with prior results 0.30 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; .

We construct entire functions with hyperbolic and simply parabolic Baker domains on which the functions are not univalent. The Riemann maps from the unit disk to these Baker domains extend continuously to certain arcs on the unit circle. The results answer questions posed by Fagella and Henriksen, Baker and Dominguez, and others.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 We construct entire functions with hyperbolic and simply parabolic Baker domains on which the functions are not univalent. contribution 0.89 0.96 0.73 asserted 1.00
s1 The Riemann maps from the unit disk to these Baker domains extend continuously to certain arcs on the unit circle. result 0.99 0.82 0.14 asserted 1.00
s2 The results answer questions posed by Fagella and Henriksen, Baker and Dominguez, and others. interpretation 0.59 0.53 0.12 asserted 1.00

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 1.00.

What was examined, and what was not

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not examined
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  • references and citing sentences
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  • P abstract
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  • T body sentences
  • C citations
  • R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original abstract

We construct entire functions with hyperbolic and simply parabolic Baker domains on which the functions are not univalent. The Riemann maps from the unit disk to these Baker domains extend continuously to certain arcs on the unit circle. The results answer questions posed by Fagella and Henriksen, Baker and Dominguez, and others.

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