Ahlfors-Schwarz lemma and curvature

Miodrag Mateljević

Displaying similar documents to “Ahlfors-Schwarz lemma and curvature”

Some properties and applications of harmonic mappings

J. H. Sampson (1978)

Annales scientifiques de l'École Normale Supérieure

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Non-Euclidean geometry and differential equations

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...

Some examples of harmonic maps for $g$ -natural metrics

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 $(M, g)$ of constant curvature and as target manifold its tangent bundle $T M$ , equipped with a suitable Riemannian $g$ -natural metric. In particular, we determine a family of Riemannian $g$ -natural metrics $G$ on $T 𝕊^{2}$ , with respect to which all conformal gradient vector fields define harmonic maps from $𝕊^{2}$ into $(T 𝕊^{2}, G)$ .

Classifications of some special infinity-harmonic maps.

Wang, Ze-Ping, Ou, Ye-Lin (2009)

Balkan Journal of Geometry and its Applications (BJGA)

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A classification and some constructions of $p$ -harmonic morphisms.

Ou, Ye-Lin, Wei, Shihshu Walter (2004)

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On weakly harmonic maps and Noether harmonic maps from a Riemann surface into a Riemannian manifold

Frédéric Hélein (1992)

Banach Center Publications

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Injectivity radius and optimal regularity of Lorentzian manifolds with bounded curvature

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. ...

Removable sets for Hölder continuous $p$ -harmonic functions on metric measure spaces.

Mäkäläinen, Tero (2008)

Annales Academiae Scientiarum Fennicae. Mathematica

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Doubly warped products with harmonic Weyl conformal curvature tensor

Andrzej Gębarowski (1994)

Colloquium Mathematicae

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