Involve: A Journal of Mathematics

  • Involve
  • Volume 4, Number 3 (2011), 271-276.

Soap film realization of isoperimetric surfaces with boundary

Jacob Ross, Donald Sampson, and Neil Steinburg

Full-text: Open access

Abstract

We examine surfaces of the type proved to be minimizing under a connectivity condition by Dorff et al. We determine which of these surfaces are stable soap films. The connectivity condition is shown to be very restrictive; few of these surfaces are stable (locally minimizing) without it.

Article information

Source
Involve, Volume 4, Number 3 (2011), 271-276.

Dates
Received: 7 April 2011
Revised: 12 April 2011
Accepted: 14 April 2011
First available in Project Euclid: 20 December 2017

Permanent link to this document
https://projecteuclid.org/euclid.involve/1513733397

Digital Object Identifier
doi:10.2140/involve.2011.4.271

Mathematical Reviews number (MathSciNet)
MR2905228

Zentralblatt MATH identifier
1248.49054

Subjects
Primary: 49Q10: Optimization of shapes other than minimal surfaces [See also 90C90]
Secondary: 49Q05: Minimal surfaces [See also 53A10, 58E12] 53A10: Minimal surfaces, surfaces with prescribed mean curvature [See also 49Q05, 49Q10, 53C42]

Keywords
bubble soap film isoperimetric equitent metacalibration minimization minimal surface area

Citation

Ross, Jacob; Sampson, Donald; Steinburg, Neil. Soap film realization of isoperimetric surfaces with boundary. Involve 4 (2011), no. 3, 271--276. doi:10.2140/involve.2011.4.271. https://projecteuclid.org/euclid.involve/1513733397


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References

  • J. Dilts, R. Dorff, and D. Sampson, “A new proof of the double bubble conjecture in $\mathbb{R}^n$”, work in progress.
  • R. Dorff, K. Fears, A. Stockman, and S. Uhl, “Solving a combined Steiner and isoperimetric problem using metacalibration”, REU Summer Research Program report, Brigham Young University, 2008.
  • R. Dorff, D. Johnson, G. R. Lawlor, and D. Sampson, “Isoperimetric surfaces with boundary”, Proc. Amer. Math. Soc. 139:12 (2011), 4467–4473.
  • R. Harvey and H. B. Lawson, Jr., “Calibrated geometries”, Acta Math. 148 (1982), 47–157.
  • F. Morgan, Geometric measure theory: A beginner's guide, Academic Press, Boston, 1988.
  • J. E. Taylor, “The structure of singularities in soap-bubble-like and soap-film-like minimal surfaces”, Ann. of Math. (2) 103:3 (1976), 489–539.