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A different expression of the Weil-Petersson potential on the quasi-Fuchsian deformation space

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Lee-Peng Teo

Complex Variables · Submitted 25 Aug 2005

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

The authors' main claim We prove that up to a constant, this function coincides with the Weil-Petersson potential on the quasi-Fuchsian deformation space.

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arXiv IDmath/0508483 (version 1)
Pith IDA7SDHA7H, Pith's permanent record of this paper and its review
CitationLee-Peng Teo. "A different expression of the Weil-Petersson potential on the quasi-Fuchsian deformation space." arXiv:math/0508483 (2005). https://pith.science/paper/A7SDHA7H
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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-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 2,907 input tokens.

What the abstract itself states, as probabilities: claims first 0.05 · states limitation 0.09 · human participants 0.01 · controlled comparison 0.03 · randomized assignment 0.01 · states quantitative result 0.57 · compares with prior results 0.33 · mentions code or data availability 0.02.

The abstract, sentence by sentence

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

We extend a definition of the Weil-Petersson potential on the universal Teichmuller space to the quasi-Fuchsian deformation space. We prove that up to a constant, this function coincides with the Weil-Petersson potential on the quasi-Fuchsian deformation space. As a result, we prove a lower bound for the Weil-Petersson potential on the quasi-Fuchsian deformation space.

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 extend a definition of the Weil-Petersson potential on the universal Teichmuller space to the quasi-Fuchsian deformation space. contribution 1.00 0.94 0.09 asserted 1.00
s1 We prove that up to a constant, this function coincides with the Weil-Petersson potential on the quasi-Fuchsian deformation space. result 0.99 0.94 0.66 asserted 1.00
s2 As a result, we prove a lower bound for the Weil-Petersson potential on the quasi-Fuchsian deformation space. result 1.00 0.95 0.34 asserted 1.00

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

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  • 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 extend a definition of the Weil-Petersson potential on the universal Teichmuller space to the quasi-Fuchsian deformation space. We prove that up to a constant, this function coincides with the Weil-Petersson potential on the quasi-Fuchsian deformation space. As a result, we prove a lower bound for the Weil-Petersson potential on the quasi-Fuchsian deformation space.

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