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Soap films bounded by non-closed curves

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Abstract

This paper proves (i) every “geometrically knotted” non-closed curve bounds a soap-film, (ii) any non-closed curve bounding a soap-film must have total curvature greater than 2π, and (iii) for every k > 2π, there is a geometrically knotted non-closed curve with total curvature k.

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Authors and Affiliations

  1. Department of Mathematics, Stanford University, 94305, Stanford, CA

    Jordan Drachman & Brian White

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  1. Jordan Drachman
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  2. Brian White
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Correspondence to Jordan Drachman.

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Drachman, J., White, B. Soap films bounded by non-closed curves. J Geom Anal 8, 239–250 (1998). https://doi.org/10.1007/BF02921642

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  • DOI: https://doi.org/10.1007/BF02921642

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