Standard realizations of crystal lattices via harmonic maps

Transactions of the American Mathematical Society

Volumn 353, Issue 1, 2001, Pages 1-20

  Kotani, Motoko ^a   Sunada, Toshikazu ^a  

^a TOHOKU UNIVERSITY   (Japan)

Author keywords

Abelian covering; Albancsc map; Albancsc torus; Crystal lattice; Harmonic map; Weighted graph

Indexed keywords

EID: 23044524360     PISSN: 00029947     EISSN: None     Source Type: Journal    
DOI: 10.1090/s0002-9947-00-02632-5     Document Type: Article

References (12)

1. B. Bollobas, Graph Theory, Springer GTM 63. MR 80j:05053
2. J. Eells, and J.H. Sampson, Harmonie 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.
4. M. Gromov and R. Schoen, Harmonic maps into singular spaces and p-adic superrigidity for lattices in groups of rank one, Publ. Math. IHES 76(1992) 165-246. MR 94e:58032
5. J. Jost, Equilibrium maps between metric spaces, Calc. Var. 2(1994) 173-204. MR 98a:58049
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.
8. M. Kotani and T. Sunada, Albanese maps and off diagonal long time asymptotics for the heat kernel, preprint.
9. T. Nagano and B. Smyth, Minimal varieties and harmonic maps in tori, Comm. Math. Helv. 50(1975), 249-265. MR 52:11797
10. H. Urakawa, A discrete analogue of the harmonic morphism and Green kernel comparison theorems, preprint.
11. E.A. Wood, Crystals and Light, An Intorduction to Optical Crystallography, Dover, 1977.
12. J. Eclls and B. Fuglede, Harmonic maps between Riemannian polyhedra, a monograph to be published.