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Numerically destabilizing minimal discs

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Nicholas Brubaker, Thomas Murphy, K. Oskar Negron

Differential Geometry · Submitted 8 Jan 2018

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

The authors' main claim We show that the set of admissible variations can be widened in a geometrically meaningful manner by considering the difference of area functional, leading to a more general notion of index.

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arXiv ID1801.02357 (version 1)
Pith IDZOYBGJLC, Pith's permanent record of this paper and its review
CitationK. Oskar Negron, Nicholas Brubaker, Thomas Murphy. "Numerically destabilizing minimal discs." arXiv:1801.02357 (2018). https://pith.science/paper/ZOYBGJLC
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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,597 input tokens.

What the abstract itself states, as probabilities: claims first 0.06 · states limitation 0.09 · human participants 0.01 · controlled comparison 0.11 · randomized assignment 0.01 · states quantitative result 0.07 · compares with prior results 0.76 · mentions code or data availability 0.02.

The abstract, sentence by sentence

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

When calculating the index of a minimal surface, the set of smooth functions on a domain with compact support is the standard setting to describe admissible variations. We show that the set of admissible variations can be widened in a geometrically meaningful manner by considering the difference of area functional, leading to a more general notion of index. This allows us to produce explicit examples of destabilizing perturbations for the fundamental Scherk surface and dihedral Enneper surfaces. In the case of dihedral Enneper surfaces we show that both the classical and our modified index can be explicitly determined.

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 When calculating the index of a minimal surface, the set of smooth functions on a domain with compact support is the standard setting to describe admissible variations. background 1.00 0.05 0.02 asserted 1.00
s1 We show that the set of admissible variations can be widened in a geometrically meaningful manner by considering the difference of area functional, leading to a more general notion of index. contribution 0.92 0.95 0.53 asserted 1.00
s2 This allows us to produce explicit examples of destabilizing perturbations for the fundamental Scherk surface and dihedral Enneper surfaces. result 0.86 0.95 0.38 asserted 0.99
s3 In the case of dihedral Enneper surfaces we show that both the classical and our modified index can be explicitly determined. result 0.93 0.95 0.16 asserted 1.00

What kind of paper the classifier reports this is: theoretical result 0.84 · evidence from proof or derivation 0.99.

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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

When calculating the index of a minimal surface, the set of smooth functions on a domain with compact support is the standard setting to describe admissible variations. We show that the set of admissible variations can be widened in a geometrically meaningful manner by considering the difference of area functional, leading to a more general notion of index. This allows us to produce explicit examples of destabilizing perturbations for the fundamental Scherk surface and dihedral Enneper surfaces. In the case of dihedral Enneper surfaces we show that both the classical and our modified index can be explicitly determined.

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