Standard realizations of crystal lattices via harmonic maps

Motoko Kotani, Toshikazu Sunada

Research output: Contribution to journalArticlepeer-review

27 Citations (Scopus)


An Eclls-Sampson typo 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.

Original languageEnglish
Pages (from-to)1-20
Number of pages20
JournalTransactions of the American Mathematical Society
Issue number1
Publication statusPublished - 2001


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

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics


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