Biharmonic maps on V-manifolds.
Chiang, Yuan-Jen, Sun, Hongan (2001)
International Journal of Mathematics and Mathematical Sciences
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Chiang, Yuan-Jen, Sun, Hongan (2001)
International Journal of Mathematics and Mathematical Sciences
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Yuan-Jen Chiang, Robert A. Wolak (2010)
Archivum Mathematicum
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In this paper, we prove that the composition of a transversal biwave map and a transversally totally geodesic map is a transversal biwave map. We show that there are biwave maps which are not transversal biwave maps, and there are transversal biwave maps which are not biwave maps either. We prove that if is a transversal biwave map satisfying certain condition, then is a transversal wave map. We finally study the transversal conservation laws of transversal biwave maps.
Todjihounde, Leonard (2006)
International Journal of Mathematics and Mathematical Sciences
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Michael Struwe (1997)
Journées équations aux dérivées partielles
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Terence Tao (2004)
Journées Équations aux dérivées partielles
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There has been much progress in recent years in understanding the existence problem for wave maps with small critical Sobolev norm (in particular for two-dimensional wave maps with small energy); a key aspect in that theory has been a renormalization procedure (either a geometric Coulomb gauge, or a microlocal gauge) which converts the nonlinear term into one closer to that of a semilinear wave equation. However, both of these renormalization procedures encounter difficulty if the energy...
Pierre H. Bérard (1977)
Mathematische Zeitschrift
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Igor Rodnianski (2005-2006)
Séminaire Bourbaki
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The paper provides a description of the wave map problem with a specific focus on the breakthrough work of T. Tao which showed that a wave map, a dynamic lorentzian analog of a harmonic map, from Minkowski space into a sphere with smooth initial data and a small critical Sobolev norm exists globally in time and remains smooth. When the dimension of the base Minkowski space is , the critical norm coincides with energy, the only manifestly conserved quantity in this (lagrangian) theory....