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Hardy inequalities in strips on ruled surfaces

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David Krejcirik

Spectral Theory · Submitted 10 Nov 2005

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

The authors' main claim We show that the negative Gauss curvature of the ambient surface gives rise to a Hardy inequality and use this to prove certain stability of spectrum in the case of asymptotically straight strips about mildly perturbed geodesics.

how it is stated · asserted 1.00 read the record →

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arXiv IDmath/0511257 (version 1)
Pith IDF6SGFAOR, Pith's permanent record of this paper and its review
CitationDavid Krejcirik. "Hardy inequalities in strips on ruled surfaces." arXiv:math/0511257 (2005). https://pith.science/paper/F6SGFAOR
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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-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 2,312 input tokens.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.31 · human participants 0.01 · controlled comparison 0.03 · randomized assignment 0.01 · states quantitative result 0.10 · compares with prior results 0.08 · mentions code or data availability 0.01.

The abstract, sentence by sentence

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

We consider the Dirichlet Laplacian in infinite two-dimensional strips defined as uniform tubular neighbourhoods of curves on ruled surfaces. We show that the negative Gauss curvature of the ambient surface gives rise to a Hardy inequality and use this to prove certain stability of spectrum in the case of asymptotically straight strips about mildly perturbed geodesics.

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 consider the Dirichlet Laplacian in infinite two-dimensional strips defined as uniform tubular neighbourhoods of curves on ruled surfaces. contribution 0.53 0.57 0.03 asserted 0.82
s1 We show that the negative Gauss curvature of the ambient surface gives rise to a Hardy inequality and use this to prove certain stability of spectrum in the case of asymptotically straight strips about mildly perturbed geodesics. result 0.76 0.95 0.87 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

sources read
  • arXiv listing abstract v1
not examined
  • full text
  • 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

We consider the Dirichlet Laplacian in infinite two-dimensional strips defined as uniform tubular neighbourhoods of curves on ruled surfaces. We show that the negative Gauss curvature of the ambient surface gives rise to a Hardy inequality and use this to prove certain stability of spectrum in the case of asymptotically straight strips about mildly perturbed geodesics.

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