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Standard realizations of crystal lattices via harmonic maps
Author(s):
Motoko
Kotani;
Toshikazu
Sunada
Journal:
Trans. Amer. Math. Soc.
353
(2001),
1-20.
MSC (2000):
Primary 58E20, 58E11, 58E30;
Secondary 82B99
Posted:
August 8, 2000
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Abstract:
An Eells-Sampson type theorem for harmonic maps from a finite weighted graph is employed to characterize the equilibrium configurations of crystals. It is thus observed that the mimimum principle frames symmetry of crystals.
References:
-
- 1.
- B. Bollobas, Graph Theory, Springer GTM 63. MR 80j:05053
- 2.
- J. Eells, Jr. and J.H. Sampson, Harmonic mappings of Riemannian manifolds, Amer. J. Math. 86(1964) 109-160. MR 29:1603
- 3.
- N. Ejiri, The second variation formula of the energy function on the Teichmüller space and the Morse index of compact minimal surfaces in tori, preprint.
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- 6.
- J. Jost, Convex functionals and generalized harmonic maps into spaces of non positive curvature, Comm. Math. Helv. 70(1995) 659-673. MR 96j:58043
- 7.
- M. Kotani and T. Sunada, Jacobian tori associated with a finite graph and its abelian covering graphs, preprint.
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Additional Information:
Motoko
Kotani
Affiliation:
Mathematical Institute, Graduate School of Science, Tôhoku University, Aoba, Sendai 980-8578, Japan
Email:
kotani@math.tohoku.ac.jp
Toshikazu
Sunada
Affiliation:
Mathematical Institute, Graduate School of Sciences, Tôhoku University, Aoba, Sendai 980-8578, Japan
Email:
sunada@math.tohoku.ac.jp
DOI:
10.1090/S0002-9947-00-02632-5
PII:
S 0002-9947(00)02632-5
Keywords:
Crystal lattice,
harmonic map,
Albanese map,
Albanese torus,
abelian covering,
weighted graph
Received by editor(s):
March 8, 1999
Posted:
August 8, 2000
Copyright of article:
Copyright
2000,
American Mathematical Society
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