Abstract
We prove that if Γ is a real-analytic Jordan curve in R3 whose total curvature does not exceed 6π, then Γ cannot bound infinitely many minimal surfaces of the topological type of the disk. This generalizes an earlier theorem of J. C. C. Nitsche, who proved the same conclusion under the additional hypothesis that Γ does not bound any minimal surface with a branch point. It should be emphasized that the theorem refers to arbitrary minimal surfaces, stable or unstable. This is the only known theorem which asserts that all members of a geometrically defined class of curves cannot bound infinitely many minimal surfaces, stable or unstable.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
