Fibrations en tores isotropes et lagrangiens
We prove fibration theorems on compact Kähler manifolds with conditions on first cohomology groups of fundamental groups with respect to unitary representations into Hilbert spaces. If the fundamental group T of compact Kähler manifold X violates Property (T) of Kazhdan’s, then for some unitary representation . By our earlier work there exists a -closed holomorphic 1-form with coefficients twisted by some unitary representation , possibly non-isomorphic to . Taking norms we obtains a positive...
We show that the length of the shortest nontrivial curve among the simple closed geodesics of index zero or one and the figure-eight geodesics of null index provides a lower bound on the area and the diameter of the Riemannian -spheres.
On généralise dans cet article la notion de filtration de Harder-Narasimhan au cas des fibrés complexes sur une variété presque complexe compacte d'une part, et au cas des faisceaux cohérents sans torsion sur une variété holomorphe d'autre part. On démontre, dans les deux cas, l'existence d'un déstabilisant maximal. On obtient un théorème de convergence en famille et par là-même l'ouverture de la stabilité en déformation.
In this article we discuss numerical scheme for the approximation of the Willmore flow of graphs. The scheme is based on the finite difference method. We improve the scheme we presented in Oberhuber [Obe-2005-2,Obe-2005-1] which is based on combination of the forward and the backward finite differences. The new scheme approximates the Willmore flow by the central differences and as a result it better preserves symmetry of the solution. Since it requires higher regularity of the solution, additional...