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Standard realizations of crystal lattices via harmonic maps


Authors: Motoko Kotani and Toshikazu Sunada
Journal: Trans. Amer. Math. Soc. 353 (2001), 1-20
MSC (2000): Primary 58E20, 58E11, 58E30; Secondary 82B99
DOI: https://doi.org/10.1090/S0002-9947-00-02632-5
Published electronically: August 8, 2000
MathSciNet review: 1783793
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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 [Enhancements On Off] (What's this?)

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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: https://doi.org/10.1090/S0002-9947-00-02632-5
Keywords: Crystal lattice, harmonic map, Albanese map, Albanese torus, abelian covering, weighted graph
Received by editor(s): March 8, 1999
Published electronically: August 8, 2000
Article copyright: © Copyright 2000 American Mathematical Society