Abstract
It is proved that any three-times continuously differentiable, nontrivial knot in three-dimensional euclidean space supports a surface that minimizes area among nearby surfaces but that does not touch all of the supporting knot. This provides a mathematical model of a physical phenomenon occurring in soap-films. The notion of a homotopically spanning surface is defined to determine an appropriate class of admissible surfaces, and it is shown that there is a lower bound on the area of admissible surfaces. The existence of an area minimizing admissible surface is then proved by the direct method based on earlier work of E. R. Reiffenberg.
Sign-in/Register to access full text options 
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.
