caa a22 4500 469117311 CHVBK 20180323133128.0 cr unu---uuuuu 170328e19920501xx s 000 0 eng 10.1007/BF02921296 doi (NATIONALLICENCE)springer-10.1007/BF02921296 Parks Harold Department of Mathematics, Oregon State University, 97331, Corvallis, OR, USA aut Soap-film-like minimal surfaces spanning knots [Elektronische Daten] [Harold Parks] 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. CRC Press, Inc, 1992 Homotopically spanning surfaces nationallicence minimal surfaces nationallicence soap-film-like surfaces nationallicence The Journal of Geometric Analysis Springer-Verlag 2/3(1992-05-01), 267-290 1050-6926 2:3<267 1992 2 12220 https://doi.org/10.1007/BF02921296 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/BF02921296 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Parks Harold Department of Mathematics, Oregon State University, 97331, Corvallis, OR, USA aut NATIONALLICENCE 773 0- The Journal of Geometric Analysis Springer-Verlag 2/3(1992-05-01), 267-290 1050-6926 2:3<267 1992 2 12220 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer