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Unbounded planar domains whose second nodal line does not touch the boundary

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P. Freitas, D. Krejcirik

Spectral Theory · Submitted 21 Nov 2005

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

The authors' main claim We show the existence of simply-connected unbounded planar domains for which the second nodal line of the Dirichlet Laplacian does not touch the boundary.

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arXiv IDmath/0511516 (version 1)
Pith IDM6B6WK2O, Pith's permanent record of this paper and its review
CitationD. Krejcirik, P. Freitas. "Unbounded planar domains whose second nodal line does not touch the boundary." arXiv:math/0511516 (2005). https://pith.science/paper/M6B6WK2O
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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 1,619 input tokens.

What the abstract itself states, as probabilities: claims first 0.05 · states limitation 0.08 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.05 · compares with prior results 0.05 · mentions code or data availability 0.02.

The abstract, sentence by sentence

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

We show the existence of simply-connected unbounded planar domains for which the second nodal line of the Dirichlet Laplacian does not touch the boundary.

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 show the existence of simply-connected unbounded planar domains for which the second nodal line of the Dirichlet Laplacian does not touch the boundary. result 0.87 0.95 0.95 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 show the existence of simply-connected unbounded planar domains for which the second nodal line of the Dirichlet Laplacian does not touch the boundary.

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