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Book Review
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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:
- [BM]
- J. Brothers and F. Morgan, The isoperimetric theorem for general integrands, Michigan Math. J. MR 1297699
- [B]
- H. Busemann, The isoperimetric problem for Minkowski area, Amer. J. Math \textbf{71} (1949), 743--762. MR 31762
- [DP]
- B. Dacorogna and C. E. Pfister, Wulff theorem and best constant in Sobolev inequality, J. Math. Pures Appl. (9) \textbf{71} (1992), 97--118. MR 1170247
- [D]
- A. Dinghas, \"Uber einen Geometrischen Satz von Wulff fur die Gleichgewichtsform von Kristallen, Z. Kristall \textbf{105} (1944), 304--314. MR 12454
- [F]
- I. Fonseca, The Wulff theorem revisited, Proc. Roy. Soc. London Ser. A \textbf{432} (1991), 125--145. MR 1116536
- [FM]
- I. Fonseca and S. Muller, A uniqueness proof for the Wulff problem, Proc. Edinburgh Math. Soc. \textbf{119A} (1991), 125--136. MR 1130601
- [G]
- M. Gage, Evolving plane curves by curvature in relative geometries, Duke Math. J. \textbf{72} (1993), 441--466. MR 1248680
- [GG]
- J. Gravner and D. Griffeath, Threshold growth dynamics, Trans. Amer. Math. Soc. \textbf{340} (1993), 837--870. MR 1147400
- [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; {\it Some theorems on the free energy of crystal surfaces\/}, Phys. Rev. {\bf 28} (1951), 87--93. MR
- [KS]
- M. Katsoulakis and P. E. Souganidis, Interacting particle systems and generalized evolution of fronts, Arch. Rational Mech. Anal. (in preparation). MR 1288808
- [M]
- F. Morgan, Geometric measure theory. A beginner\RM 's guide, Academic Press, New York, 1988. MR 933756
- [O]
- R. Osserman, The isoperimetric inequality, Bull. Amer. Math. Soc. \textbf{84} (1978), 1182--1238. MR 500557
- [P]
- C. E. Pfister, Long deviations and phase separation in the two-dimensional Ising model, Helv. Phys. Acta \textbf{64} (1991), 953--1054. MR 1149430
- [R]
- R. T. Rockafellar, Convex analysis, Princeton Univ. Press, Princeton, NJ, 1970. MR 274683
- [T]
- J. E. Taylor, \emph{Existence and structure of solutions to a class of nonelliptic variational problems}, Academic Press, London, 1974 pp.~499--508. MR 420407
- [TCH]
- J. E. Taylor, J. W. Cahn, and C. A. Handwerker, Geometric models of crystal growth, Acta Met. Mat. \textbf{40} (1992), 1443--1474. MR
- [W]
- G. Wulff, Zur frage der Geschwindigkeit des Wachstums und der Auflosung der Krystalflachen, Z. Krist. \textbf{34} (1901), 449. MR
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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