Some properties and applications of harmonic mappings
J. H. Sampson (1978)
Annales scientifiques de l'École Normale Supérieure
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J. H. Sampson (1978)
Annales scientifiques de l'École Normale Supérieure
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A. Popov (1996)
Banach Center Publications
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In this paper a geometrical link between partial differential equations (PDE) and special coordinate nets on two-dimensional smooth manifolds with the a priori given curvature is suggested. The notion of G-class (the Gauss class) of differential equations admitting such an interpretation is introduced. The perspective of this approach is the possibility of applying the instruments and methods of non-Euclidean geometry to the investigation of differential equations. The equations generated...
Mohamed Tahar Kadaoui Abbassi, Giovanni Calvaruso, Domenico Perrone (2009)
Annales mathématiques Blaise Pascal
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We produce new examples of harmonic maps, having as source manifold a space of constant curvature and as target manifold its tangent bundle , equipped with a suitable Riemannian -natural metric. In particular, we determine a family of Riemannian -natural metrics on , with respect to which all conformal gradient vector fields define harmonic maps from into .
Wang, Ze-Ping, Ou, Ye-Lin (2009)
Balkan Journal of Geometry and its Applications (BJGA)
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Ou, Ye-Lin, Wei, Shihshu Walter (2004)
Beiträge zur Algebra und Geometrie
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Frédéric Hélein (1992)
Banach Center Publications
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Philippe G. LeFloch (2007-2008)
Séminaire de théorie spectrale et géométrie
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We review recent work on the local geometry and optimal regularity of Lorentzian manifolds with bounded curvature. Our main results provide an estimate of the injectivity radius of an observer, and a local canonical foliations by CMC (Constant Mean Curvature) hypersurfaces, together with spatially harmonic coordinates. In contrast with earlier results based on a global bound for derivatives of the curvature, our method requires only a sup-norm bound on the curvature near the given observer. ...
Mäkäläinen, Tero (2008)
Annales Academiae Scientiarum Fennicae. Mathematica
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Andrzej Gębarowski (1994)
Colloquium Mathematicae
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