A Free Boundary Minimal Surface via a 6-Sweepout

We prove that the Almgren–Pitts 6-width of the unit 3-ball is less than 2 π . We also prove that there exists a free boundary minimal surface in the unit 3-ball that has genus at most 1, index at most 5, area less than 2 π , and is not the equatorial disk or the critical catenoid.

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Veröffentlicht in:	The Journal of Geometric Analysis 2023-07, Vol.33 (7), Article 230
1. Verfasser:	Chu, Adrian Chun-Pong
Format:	Artikel
Sprache:	eng
Schlagworte:	Abstract Harmonic Analysis Convex and Discrete Geometry Differential Geometry Dynamical Systems and Ergodic Theory Fourier Analysis Free boundaries Geometry Global Analysis and Analysis on Manifolds Mathematics Mathematics and Statistics Minimal surfaces
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Beschreibung
Zusammenfassung:	We prove that the Almgren–Pitts 6-width of the unit 3-ball is less than 2 π . We also prove that there exists a free boundary minimal surface in the unit 3-ball that has genus at most 1, index at most 5, area less than 2 π , and is not the equatorial disk or the critical catenoid.
ISSN:	1050-6926 1559-002X
DOI:	10.1007/s12220-023-01285-y