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On boundary behavior of one class of mappings on Riemannian manifolds

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Evgeny Sevost'yanov

Complex Variables · Submitted 13 Apr 2015

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

The authors' main claim Theorems on continuous extension on boundary for one class of open discrete mappings between Riemannian manifolds are obtained.

how it is stated · asserted 1.00 read the record →

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arXiv ID1504.03295 (version 1)
Pith IDOVVRL4TT, Pith's permanent record of this paper and its review
CitationEvgeny Sevost'yanov. "On boundary behavior of one class of mappings on Riemannian manifolds." arXiv:1504.03295 (2015). https://pith.science/paper/OVVRL4TT
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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, 2,388 input tokens, $0.0001 reported.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.34 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.07 · compares with prior results 0.04 · mentions code or data availability 0.01.

The abstract, sentence by sentence

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

Theorems on continuous extension on boundary for one class of open discrete mappings between Riemannian manifolds are obtained. In particular, there is proved that, open discrete ring $Q$-mappings $f:D\rightarrow D^{\,\prime}$ are extend to $\partial D$ whenever $\partial D$ is locally connected, $\partial D^{\,\prime}$ is strongly accessible, and a function $Q$ has finite mean oscillation at $\partial D.$

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 Theorems on continuous extension on boundary for one class of open discrete mappings between Riemannian manifolds are obtained. result 0.55 0.92 0.73 asserted 1.00
s1 In particular, there is proved that, open discrete ring $Q$-mappings $f:D\rightarrow D^{\,\prime}$ are extend to $\partial D$ whenever $\partial D$ is locally connected, $\partial D^{\,\prime}$ is strongly accessible, and a function $Q$ has finite mean oscillation at $\partial D.$ result 0.99 0.92 0.70 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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  • 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

Theorems on continuous extension on boundary for one class of open discrete mappings between Riemannian manifolds are obtained. In particular, there is proved that, open discrete ring $Q$-mappings $f:D\rightarrow D^{\,\prime}$ are extend to $\partial D$ whenever $\partial D$ is locally connected, $\partial D^{\,\prime}$ is strongly accessible, and a function $Q$ has finite mean oscillation at $\partial D.$

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