-minimal curve regularity
Author:
Frank Morgan
Journal:
Proc. Amer. Math. Soc. 120 (1994), 677-686
MSC:
Primary 49Q20; Secondary 58E12
DOI:
https://doi.org/10.1090/S0002-9939-1994-1169884-3
MathSciNet review:
1169884
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Abstract | References | Similar Articles | Additional Information
Abstract: -minimal sets are embedded
curves meeting in threes at 120
angles.
- [A] F. J. Almgren Jr., Existence and regularity almost everywhere of solutions to elliptic variational problems with constraints, Mem. Amer. Math. Soc. 4 (1976), no. 165, viii+199. MR 0420406, https://doi.org/10.1090/memo/0165
- [F] Herbert Federer, Geometric measure theory, Die Grundlehren der mathematischen Wissenschaften, Band 153, Springer-Verlag New York Inc., New York, 1969. MR 0257325
- [LM] Gary Lawlor and Frank Morgan, Paired calibrations applied to soap films, immiscible fluids, and surfaces or networks minimizing other norms, Pacific J. Math. 166 (1994), no. 1, 55–83. MR 1306034
- [M1] Frank Morgan, Geometric measure theory, Academic Press, Inc., Boston, MA, 1988. A beginner’s guide. MR 933756
- [M2]
-, Soap bubbles in
and in surfaces, Pacific J. Math. (to appear).
- [M3] Frank Morgan, Size-minimizing rectifiable currents, Invent. Math. 96 (1989), no. 2, 333–348. MR 989700, https://doi.org/10.1007/BF01393966
- [M4] -, Soap bubbles and soap films, Mathematical Vistas: New and Recent Publications in Mathematics from the New York Academy of Sciences (Joseph Malkevitch and Donald McCarthy, eds.), vol. 607, New York Acad. Sci., New York, 1990, pp. 98-106.
- [T] Jean E. Taylor, The structure of singularities in soap-bubble-like and soap-film-like minimal surfaces, Ann. of Math. (2) 103 (1976), no. 3, 489–539. MR 428181, https://doi.org/10.2307/1970949
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Additional Information
DOI:
https://doi.org/10.1090/S0002-9939-1994-1169884-3
Keywords:
-minimal,
minimal curves
Article copyright:
© Copyright 1994
American Mathematical Society