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On the cauchy problem for harmonic maps defined on two‐dimensional Minkowski space
Author(s) -
ChaoHao Gu
Publication year - 1980
Publication title -
communications on pure and applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.12
H-Index - 115
eISSN - 1097-0312
pISSN - 0010-3640
DOI - 10.1002/cpa.3160330604
Subject(s) - minkowski space , mathematics , harmonic map , riemannian manifold , cauchy distribution , space (punctuation) , pure mathematics , dimension (graph theory) , manifold (fluid mechanics) , mathematical analysis , field (mathematics) , minkowski's theorem , harmonic function , harmonic , mathematical physics , physics , quantum mechanics , mechanical engineering , linguistics , philosophy , engineering
Let R 1+1 be two‐dimensional Minkowski space and M a complete Riemannian manifold of dimension n . It is proved that the solution of the Cauchy problem for the harmonic map ϕ : R 1+1 → M exists globally. As an application to physics we conclude that the field function in a two‐dimensional chiral field theory is regular for all time, if it is regular initially.