Minimizing Harmonic Mappings form a surface perfored with small holes into a riemannian manifold.
Sami Baraket, Dong Ye (1992)
Manuscripta mathematica
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Sami Baraket, Dong Ye (1992)
Manuscripta mathematica
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Choi, Gundon, Yun, Gabjin (2005)
International Journal of Mathematics and Mathematical Sciences
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Bent Fuglede (1978)
Annales de l'institut Fourier
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A harmonic morphism between Riemannian manifolds and is by definition a continuous mappings which pulls back harmonic functions. It is assumed that dim dim, since otherwise every harmonic morphism is constant. It is shown that a harmonic morphism is the same as a harmonic mapping in the sense of Eells and Sampson with the further property of being semiconformal, that is, a conformal submersion of the points where vanishes. Every non-constant harmonic morphism is shown to be...
Ilkka Holopainen, Seppo Rickman (1992)
Revista Matemática Iberoamericana
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Tsagas, Gr., Bitis, Gr. (2001)
Balkan Journal of Geometry and its Applications (BJGA)
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Atsushi Tachikawa (1987)
Journal für die reine und angewandte Mathematik
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George Paulik (1988)
Manuscripta mathematica
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Atsushi Tachikawa (1992)
Manuscripta mathematica
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B. Bojarski, T. Iwaniec (1987)
Banach Center Publications
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Michael Struwe (1991)
Manuscripta mathematica
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Robert E. Greene, H. Wu (1975)
Annales de l'institut Fourier
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Let be a noncompact Riemannian manifold of dimension . Then there exists a proper embedding of into by harmonic functions on . It is easy to find harmonic functions which give an embedding. However, it is more difficult to achieve properness. The proof depends on the theorems of Lax-Malgrange and Aronszajn-Cordes in the theory of elliptic equations.