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Fibrations of compact Kähler manifolds in terms of cohomological properties of their fundamental groups

Ngaiming Mok (2000)

Annales de l'institut Fourier

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 H 1 ( G a m m a , Φ ) ≠ 0 for some unitary representation Φ . By our earlier work there exists a d -closed holomorphic 1-form with coefficients twisted by some unitary representation Φ ' , possibly non-isomorphic to Φ . Taking norms we obtains a positive...

Filling Radius and Short Closed Geodesics of the 2 -Sphere

Stéphane Sabourau (2004)

Bulletin de la Société Mathématique de France

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 2 -spheres.

Filtration de Harder-Narasimhan pour des fibrés complexes ou des faisceaux sans torsion

Laurent Bruasse (2003)

Annales de l’institut Fourier

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.

Finite difference scheme for the Willmore flow of graphs

Tomáš Oberhuber (2007)

Kybernetika

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...

Finite group actions on 2- dimensional CW-complexes

Dorabiala, Wojciech (1994)

Proceedings of the Winter School "Geometry and Physics"

Let X be a cell complex obtained by attaching a 2-cell to a finite bouquet of circles (for example, a closed surface). In terms of the combinatorial type of the attaching map, the paper gives conditions for the existence of a fixed point free (topological) homeomorphism of the complex X . Also, quotients of finite group actions on such complexes are considered as well as a condition under which the induced actions on cohomology are trivial.

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