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Isoperimetric surfaces with boundary


Authors: Rebecca Dorff, Drew Johnson, Gary R. Lawlor and Donald Sampson
Journal: Proc. Amer. Math. Soc. 139 (2011), 4467-4473
MSC (2010): Primary 53C38; Secondary 49Q10
Published electronically: April 26, 2011
MathSciNet review: 2823092
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Abstract: We prove that many common combinations of soap films and soap bubbles that result from dipping polyhedral wire frames in a soap solution are minimizing with respect to their boundary and bubble volume. This can be thought of as a combination of the Plateau problem of least area for surfaces spanning a given boundary and the isoperimetric problem of least area for surfaces enclosing a given volume. Proof is given in arbitrary dimension using a combination of the mapping of Gromov, after Knothe, and the paired calibrations of Lawlor and Morgan.


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Additional Information

Rebecca Dorff
Affiliation: Department of Mathematics, Brigham Young University, Provo, Utah 84604
Email: beccadorff@gmail.com

Drew Johnson
Affiliation: Department of Mathematics, Brigham Young University, Provo, Utah 84604
Email: werd2.718@gmail.com

Gary R. Lawlor
Affiliation: Department of Mathematics, Brigham Young University, Provo, Utah 84604
Email: lawlor@mathed.byu.edu

Donald Sampson
Affiliation: Department of Mathematics, Brigham Young University, Provo, Utah 84604
Email: sampson.dcs@gmail.com

DOI: https://doi.org/10.1090/S0002-9939-2011-10872-4
Keywords: Metacalibration, calibration, isoperimetric, equitent
Received by editor(s): October 8, 2010
Received by editor(s) in revised form: October 20, 2010
Published electronically: April 26, 2011
Communicated by: Jianguo Cao
Article copyright: © Copyright 2011 American Mathematical Society