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
Full-text PDF Free Access
Abstract | References | Similar Articles | Additional Information
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.
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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
MR Author ID:
168895
Email:
sunada@math.tohoku.ac.jp
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
