A smooth Jordan curve spanning infinitely many stable minimal disks

This paper gives a negative answer to Problem 93 for immersed minimal surfaces. It constructs a smooth regular Jordan curve in three-dimensional Euclidean space that spans infinitely many strictly stable immersed minimal disks with pairwise distinct geometric images. Their areas increase strictly and converge to a finite limit. Repository: https://github.com/opensource120/Some-Answers-to-Yau-s-120-open-problems-in-geometryPDF at the deposited version: https://github.com/opensource120/Some-Answers-to-Yau-s-120-open-problems-in-geometry/blob/b4f17a71d1712073bf82196a01c29ae04292e5c1/papers/problem_93_stable_minimal_disks.pdfTeX source at the deposited version: https://github.com/opensource120/Some-Answers-to-Yau-s-120-open-problems-in-geometry/blob/b4f17a71d1712073bf82196a01c29ae04292e5c1/papers/stable_minimal_disks.tex

Authors

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-11-06
DOI
https://doi.org/10.5281/zenodo.23984948
Primary Topic
Geometric Analysis and Curvature Flows
Type
preprint
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preprint

A smooth Jordan curve spanning infinitely many stable minimal disks

opensource120
Zenodo (CERN European Organization for Nuclear Research)
Geometric Analysis and Curvature Flows
preprint

A smooth Jordan curve spanning infinitely many stable minimal disks

opensource120
preprint en

Abstract

This paper gives a negative answer to Problem 93 for immersed minimal surfaces. It constructs a smooth regular Jordan curve in three-dimensional Euclidean space that spans infinitely many strictly stable immersed minimal disks with pairwise distinct geometric images. Their areas increase strictly and converge to a finite limit. Repository: https://github.com/opensource120/Some-Answers-to-Yau-s-120-open-problems-in-geometryPDF at the deposited version: https://github.com/opensource120/Some-Answers-to-Yau-s-120-open-problems-in-geometry/blob/b4f17a71d1712073bf82196a01c29ae04292e5c1/papers/problem_93_stable_minimal_disks.pdfTeX source at the deposited version: https://github.com/opensource120/Some-Answers-to-Yau-s-120-open-problems-in-geometry/blob/b4f17a71d1712073bf82196a01c29ae04292e5c1/papers/stable_minimal_disks.tex

Zenodo (CERN European Organization for Nuclear Research)
Geometric Analysis and Curvature Flows
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