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 | References | Similar Articles | Additional Information

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