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On the harmonic M\"obius transformations

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Rodrigo Hernández, María J. Martín

Complex Variables · Submitted 16 Oct 2017

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

The authors' main claim In this paper, we identify completely the relationship between two locally univalent harmonic mappings with equal (harmonic) Schwarzian derivative.

how it is stated · asserted 1.00 read the record →

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arXiv ID1710.05952 (version 1)
Pith IDG5YF6B4F, Pith's permanent record of this paper and its review
CitationMar\'ia J. Mart\'in, Rodrigo Hern\'andez. "On the harmonic M\"obius transformations." arXiv:1710.05952 (2017). https://pith.science/paper/G5YF6B4F
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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, 2,330 input tokens.

What the abstract itself states, as probabilities: claims first 0.09 · states limitation 0.07 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.03 · compares with prior results 0.83 · mentions code or data availability 0.01.

The abstract, sentence by sentence

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

It is well-known that two locally univalent analytic functions $\varphi$ and $\psi$ have equal Schwarzian derivative if and only if there exists a non-constant M\"obius transformation $T$ such that $\varphi=T\circ \psi$. In this paper, we identify completely the relationship between two locally univalent harmonic mappings with equal (harmonic) Schwarzian derivative.

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 It is well-known that two locally univalent analytic functions $\varphi$ and $\psi$ have equal Schwarzian derivative if and only if there exists a non-constant M\"obius transformation $T$ such that $\varphi=T\circ \psi$. background 1.00 0.03 0.04 asserted 1.00
s1 In this paper, we identify completely the relationship between two locally univalent harmonic mappings with equal (harmonic) Schwarzian derivative. contribution 0.94 0.95 0.61 asserted 1.00

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 0.99.

What was examined, and what was not

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  • figures and tables
  • references and citing sentences
  • relations to other papers
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  • P abstract
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  • S sections
  • 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

It is well-known that two locally univalent analytic functions $\varphi$ and $\psi$ have equal Schwarzian derivative if and only if there exists a non-constant M\"obius transformation $T$ such that $\varphi=T\circ \psi$. In this paper, we identify completely the relationship between two locally univalent harmonic mappings with equal (harmonic) Schwarzian derivative.

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Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

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Cites as background 3 papers

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