Isoperimetric surfaces with boundary

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...

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Bibliographic Details
Published in:Proceedings of the American Mathematical Society 2011-12, Vol.139 (12), p.4467-4473
Main Authors: DORFF, REBECCA, JOHNSON, DREW, LAWLOR, GARY R., SAMPSON, DONALD
Format: Article
Language:English
Subjects:
Calibration
College mathematics
Exact sciences and technology
General mathematics
General, history and biography
Isoperimetric problem
Lamps
Mathematical surfaces
Mathematics
Nonparametric inference
Polytopes
Probability and statistics
Sciences and techniques of general use
Soaps
Statistics
Vector fields
Vertices
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Summary: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.
ISSN:0002-9939
1088-6826
DOI:10.1090/S0002-9939-2011-10872-4