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The infinitesimal earthquake theorem for vector fields on the circle

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Farid Diaf

Geometric Topology · Submitted 2 Nov 2023

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

The authors' main claim We prove that any continuous vector field on a circle is the extension in a suitable sense, of a unique infinitesimal earthquake of the hyperbolic plane.

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arXiv ID2311.01262 (version 2)
Pith IDLXP3JF7Q, Pith's permanent record of this paper and its review
CitationFarid Diaf. "The infinitesimal earthquake theorem for vector fields on the circle." arXiv:2311.01262 (2023). https://pith.science/paper/LXP3JF7Q
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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, 4,246 input tokens.

What the abstract itself states, as probabilities: claims first 0.22 · states limitation 0.24 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.06 · compares with prior results 0.86 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v2. Results and the main claim are underlined; .

We prove that any continuous vector field on a circle is the extension in a suitable sense, of a unique infinitesimal earthquake of the hyperbolic plane. Furthermore, we obtain other extension results when the vector field is assumed only to be upper or lower semicontinuous. This leads to a generalization of Kerckhoff's and Gardiner's infinitesimal earthquake theorems to a broader setting, using a completely novel approach. The proof is based on the geometry of the dual of Minkowski three-space, also called Half-pipe three-geometry. In this way, we obtain a simple characterization of Zygmund vector fields on the circle in terms of width of convex hulls.

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 prove that any continuous vector field on a circle is the extension in a suitable sense, of a unique infinitesimal earthquake of the hyperbolic plane. result 0.90 0.96 0.92 asserted 1.00
s1 Furthermore, we obtain other extension results when the vector field is assumed only to be upper or lower semicontinuous. result 0.90 0.95 0.06 asserted 1.00
s2 This leads to a generalization of Kerckhoff's and Gardiner's infinitesimal earthquake theorems to a broader setting, using a completely novel approach. contribution 0.55 0.93 0.16 asserted 1.00
s3 The proof is based on the geometry of the dual of Minkowski three-space, also called Half-pipe three-geometry. method 1.00 0.60 0.03 asserted 1.00
s4 In this way, we obtain a simple characterization of Zygmund vector fields on the circle in terms of width of convex hulls. result 0.96 0.94 0.09 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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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 prove that any continuous vector field on a circle is the extension in a suitable sense, of a unique infinitesimal earthquake of the hyperbolic plane. Furthermore, we obtain other extension results when the vector field is assumed only to be upper or lower semicontinuous. This leads to a generalization of Kerckhoff's and Gardiner's infinitesimal earthquake theorems to a broader setting, using a completely novel approach. The proof is based on the geometry of the dual of Minkowski three-space, also called Half-pipe three-geometry. In this way, we obtain a simple characterization of Zygmund vector fields on the circle in terms of width of convex hulls.

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