The search session has expired. Please query the service again.
The search session has expired. Please query the service again.
The search session has expired. Please query the service again.
The search session has expired. Please query the service again.
The search session has expired. Please query the service again.
The search session has expired. Please query the service again.
The search session has expired. Please query the service again.
The search session has expired. Please query the service again.
We give here a generalization of the theory of optimal destabilizing 1-parameter
subgroups to non algebraic complex geometry : we consider holomorphic actions of a
complex reductive Lie group on a finite dimensional (possibly non compact) Kähler
manifold. In a second part we show how these results may extend in the gauge theoretical
framework and we discuss the relation between the Harder-Narasimhan filtration and the
optimal detstabilizing vectors of a non semistable object....
We study representations of lattices of into . We show that if a representation is reductive and if is at least 2, then there exists a finite energy harmonic equivariant map from complex hyperbolic -space to complex hyperbolic -space. This allows us to give a differential geometric proof of rigidity results obtained by M. Burger and A. Iozzi. We also define a new invariant associated to representations into of non-uniform lattices in , and more generally of fundamental groups of orientable...
We define a functional for Hermitian metrics using the curvature of the Chern connection. The Euler–Lagrange equation for this functional is an elliptic equation for Hermitian metrics. Solutions to this equation are related to Kähler–Einstein metrics, and are automatically Kähler–Einstein under certain conditions. Given this, a natural parabolic flow equation arises. We prove short time existence and regularity results for this flow, as well as stability for the flow near Kähler–Einstein metrics...
We study Hölder continuity of solutions to the Monge-Ampère equations on compact Kähler manifolds. T. C. Dinh, V.A. Nguyen and N. Sibony have shown that the measure is moderate if is Hölder continuous. We prove a theorem which is a partial converse to this result.
Let be a compact Kähler manifold. We obtain uniform Hölder regularity for solutions to the complex Monge-Ampère equation on with right hand side, . The same regularity is furthermore proved on the ample locus in any big cohomology class. We also study the range of the complex Monge-Ampère operator acting on -plurisubharmonic Hölder continuous functions. We show that this set is convex, by sharpening Kołodziej’s result that measures with -density belong to and proving that has the...
Let be an open set of a Stein manifold of dimension such that for . We prove that is Stein if and only if every topologically trivial holomorphic line bundle on is associated to some Cartier divisor on .
Holomorphic Poisson structures arise naturally in the realm of generalized geometry. A holomorphic Poisson structure induces a deformation of the complex structure in a generalized sense, whose cohomology is obtained by twisting the Dolbeault @-operator by the holomorphic Poisson bivector field. Therefore, the cohomology space naturally appears as the limit of a spectral sequence of a double complex. The first sheet of this spectral sequence is simply the Dolbeault cohomology with coefficients in...
Currently displaying 1 –
20 of
26