Book Review
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MathSciNet review:
1181197
Full text of review:
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Book Information:
Author:
R. Kotecky R. Dobrushin, 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.
John E. Brothers and Frank Morgan, The isoperimetric theorem for general integrands, Michigan Math. J. 41 (1994), no. 3, 419–431. MR 1297699, DOI 10.1307/mmj/1029005070
Herbert Busemann, The isoperimetric problem for Minkowski area, Amer. J. Math. 71 (1949), 743–762. MR 31762, DOI 10.2307/2372362
B. Dacorogna and C.-E. Pfister, Wulff theorem and best constant in Sobolev inequality, J. Math. Pures Appl. (9) 71 (1992), no. 2, 97–118. MR 1170247
Alexander Dinghas, Über einen geometrischen Satz von Wulff für die Gleichgewichtsform von Kristallen, Z. Kristallogr., Mineral. Petrogr. 105 (1944), no. Abt. A., 304–314 (German). MR 0012454
Irene Fonseca, The Wulff theorem revisited, Proc. Roy. Soc. London Ser. A 432 (1991), no. 1884, 125–145. MR 1116536, DOI 10.1098/rspa.1991.0009
Irene Fonseca and Stefan Müller, A uniqueness proof for the Wulff theorem, Proc. Roy. Soc. Edinburgh Sect. A 119 (1991), no. 1-2, 125–136. MR 1130601, DOI 10.1017/S0308210500028365
Michael E. Gage, Evolving plane curves by curvature in relative geometries, Duke Math. J. 72 (1993), no. 2, 441–466. MR 1248680, DOI 10.1215/S0012-7094-93-07216-X
Janko Gravner and David Griffeath, Threshold growth dynamics, Trans. Amer. Math. Soc. 340 (1993), no. 2, 837–870. MR 1147400, DOI 10.1090/S0002-9947-1993-1147400-3
[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.
Markos A. Katsoulakis and Panagiotis E. Souganidis, Interacting particle systems and generalized evolution of fronts, Arch. Rational Mech. Anal. 127 (1994), no. 2, 133–157. MR 1288808, DOI 10.1007/BF00377658
Frank Morgan, Geometric measure theory, Academic Press, Inc., Boston, MA, 1988. A beginner’s guide. MR 933756
Robert Osserman, The isoperimetric inequality, Bull. Amer. Math. Soc. 84 (1978), no. 6, 1182–1238. MR 500557, DOI 10.1090/S0002-9904-1978-14553-4
C.-E. Pfister, Large deviations and phase separation in the two-dimensional Ising model, Helv. Phys. Acta 64 (1991), no. 7, 953–1054. MR 1149430
R. Tyrrell Rockafellar, Convex analysis, Princeton Mathematical Series, No. 28, Princeton University Press, Princeton, N.J., 1970. MR 0274683
Jean E. Taylor, Existence and structure of solutions to a class of nonelliptic variational problems, Symposia Mathematica, Vol. XIV (Convegno di Teoria Geometrica dell’Integrazione e Varietà Minimali, INDAM, Roma, Maggio 1973), Academic Press, London, 1974, pp. 499–508. MR 0420407
[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.
- [BM]
- 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.
Review Information:
Reviewer:
Jean E. Taylor
Journal:
Bull. Amer. Math. Soc.
31 (1994), 291-296
DOI:
https://doi.org/10.1090/S0273-0979-1994-00535-X
