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Original Articles

Numerical Solution of Soap Film Dual Problems

Pages 269-287 | Published online: 03 Apr 2012

REFERENCES

  • Andersen , K. D. 1995 . “Minimizing a sum of norms” , Ph.D. Thesis Odense University. . [Andersen 1995]
  • Brakke , K. A. 1991 . “Minimal cones on hypercubes” . J. Geom. Anal. , 1 : 329 – 338 . [Brakke 1991]
  • Brakke , K. A. 1992 . “The Surface Evolver” . Experimental Mathematics , 1 : 141 – 165 . [Brakke 1992]
  • Brakke , K. A. “Soap films and covering spaces” [Brakke 1995], to appear in J. Geom. Anal. Preprint available at http://www.geom.umn.edu/docs/preprints/online/GCG54.html
  • Federer , H. 1969 . Geometric measure theory Berlin : Springer. . [Federer 1969], Grundlehren der mathematischen Wissenschaften 153
  • Federer , H. 1974 . “Real flat chains, cochains and variational problems” . Indiana U. Math. J. , 24 : 351 – 407 . [Federer 1974]
  • Giusti , E. 1984 . Minimal surfaces and functions of bounded variation Boston : Birkhäuser. . [Giusti 1984]
  • Harvey , R. and Lawson , H. B. Jr. 1982 . “Calibrated geometries” . Acta Math. , 148 : 47 – 157 . [Harvey and Lawson 1982]
  • Lawlor , G. and Morgan , F. 1994 . “Paired calibrations applied to soap films, immiscible fluids, and surfaces or networks minimizing other norms” . Pacific J. of Math. , 166 : 55 – 83 . [Lawlor and Morgan 1994]
  • Morgan , F. 1995 . Geometric Measure Theory: A Beginner's Guide, , 2nd ed. Boston : Academic Press. . [Morgan 1995]
  • Parks , H. R. 1977 . “Explicit determination of area minimizing hypersurfaces” . Duke Math. J. , 44 : 519 – 534 . [Parks 1977]
  • Parks , H. R. 1986 . “Explicit determination of area minimizing hypersurfaces II” . Mem. Amer. Math. Soc. , 342 : 90 [Parks 1986]
  • Parks , H. R. 1992 . “Numerical approximation of parametric area-minimizing hypersurfaces” . SIAM J. Sci. Stat. Comput. , 13 : 499 – 511 . [Parks 1992]
  • Parks , H. R. and Pitts , J. T. “Computing least area hypersurfaces spanning arbitrary boundaries” [Parks and Pitts 1997], to appear in SIAM J. Sci. Comput. (preprint available from editors at [email protected], [email protected])
  • [Phillips et al. 1993] . “Geomview: an interactive geometry viewer” . Notices Amer. Math. Soc. , 985 – 988 . See also Electronic Availability below
  • Sullivan , J. M. 1990 . A crystalline approximation theorem for hypersurfaces , Ph.D. Thesis Princeton University. . [Sullivan 1990]
  • Sullivan , J. M. “Convex deltatopes in all dimensions, and polyhedral soap films” [Sullivan 1995], preprint available from the editor ([email protected])
  • Taylor , J. E. 1976 . “The structure of singularities in soap-bubble-like and soap-film-like minimal surfaces” . Ann. of Math. , 103 : 489 – 539 . [Taylor 1976]
  • Underwood , A. 1993 . “Constructing barriers to minimal surfaces from polyhedral data” , Ph.D. Thesis Princeton University. . [Underwood 1993]

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