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Book Review
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MathSciNet review:
1181197
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Book Information
Author(s):
R. Dobrushin, R. Kotecky, and S. Shlosman
Title:
Wulff construction, A global shape from local interaction
Additional book information:
American Mathematical Society, Providence, RI, 1992, ix + 204 pp., US$130.00. ISBN 0-8218-4563-2
References:
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- J. Brothers and F. Morgan, The isoperimetric theorem for general integrands, Michigan Math. J. (to appear). MR 1297699 (95g:49080)
- [B]
- H. Busemann, The isoperimetric problem for Minkowski area, Amer. J. Math 71 (1949), 743-762. MR 0031762 (11:200j)
- [DP]
- B. Dacorogna and C. E. Pfister, Wulff theorem and best constant in Sobolev inequality, J. Math. Pures Appl. (9) 71 (1992), 97-118. MR 1170247 (94d:49070)
- [D]
- A. Dinghas, Über einen Geometrischen Satz von Wulff fur die Gleichgewichtsform von Kristallen, Z. Kristall 105 (1944), 304-314 MR 0012454 (7:25d)
- [F]
- I. Fonseca, The Wulff theorem revisited, Proc. Roy. Soc. London Ser. A 432 (1991), 125-145. MR 1116536 (92e:49053)
- [FM]
- I. Fonseca and S. Muller, A uniqueness proof for the Wulff problem, Proc. Edinburgh Math. Soc. 119A (1991), 125-136. MR 1130601 (93c:49026)
- [G]
- M. Gage, Evolving plane curves by curvature in relative geometries, Duke Math. J. 72 (1993), 441-466. MR 1248680 (94j:53001)
- [GG]
- J. Gravner and D. Griffeath, Threshold growth dynamics, Trans. Amer. Math. Soc. 340 (1993), 837-870. MR 1147400 (94b:52006)
- [H]
- C. Herring, The use of classical macroscopic concepts in surface energy problems, Structure and Properties of Solid Surfaces (R. Gomer, ed.), Univ. of Chicago Press, Chicago, 1952, pp. 5-73; Some theorems on the free energy of crystal surfaces, Phys. Rev. 28 (1951), 87-93.
- [KS]
- M. Katsoulakis and P. E. Souganidis, Interacting particle systems and generalized evolution of fronts, Arch. Rational Mech. Anal. (in preparation). MR 1288808 (95h:82023)
- [M]
- F. Morgan, Geometric measure theory. A beginner's guide, Academic Press, New York, 1988. MR 933756 (89f:49036)
- [O]
- R. Osserman, The isoperimetric inequality, Bull. Amer. Math. Soc. 84 (1978), 1182-1238. MR 0500557 (58:18161)
- [P]
- C. E. Pfister, Long deviations and phase separation in the two-dimensional Ising model, Helv. Phys. Acta 64 (1991), 953-1054. MR 1149430 (93c:82011)
- [R]
- R. T. Rockafellar, Convex analysis, Princeton Univ. Press, Princeton, NJ, 1970. MR 0274683 (43:445)
- [T]
- J. E. Taylor, Existence and structure of solutions to a class of nonelliptic variational problems, Sympos. Math., vol. 14, Academic Press, London, 1974, pp. 499-508; Unique structure of solutions to a class of nonelliptic variational problems, Proc. Sympos. Pure Math., vol. XXVII, Amer. Math. Soc., Providence, RI, 1974, pp. 481-489. MR 0420407 (54:8421)
- [TCH]
- J. E. Taylor, J. W. Cahn, and C. A. Handwerker, Geometric models of crystal growth, Acta Met. Mat. 40 (1992), 1443-1474.
- [W]
- G. Wulff, Zur frage der Geschwindigkeit des Wachstums und der Auflosung der Krystal-flachen, Z. Krist. 34 (1901), 449.
Additional Information:
Reviewer(s):
Jean E.
Taylor
Review Information:
Journal:
Bull. Amer. Math. Soc.
31
(1994),
291-296.
DOI:
10.1090/S0273-0979-1994-00535-X
PII:
S 0273-0979(1994)00535-X
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