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Harder-Narasimhan filtrations and optimal destabilizing vectors in complex geometry

Laurent Bruasse, Andrei Teleman (2005)

Annales de l’institut Fourier

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....

Harmonic maps and representations of non-uniform lattices of $PU (m, 1)$

Vincent Koziarz, Julien Maubon (2008)

Annales de l’institut Fourier

We study representations of lattices of $PU (m, 1)$ into $PU (n, 1)$ . We show that if a representation is reductive and if $m$ is at least 2, then there exists a finite energy harmonic equivariant map from complex hyperbolic $m$ -space to complex hyperbolic $n$ -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 $PU (n, 1)$ of non-uniform lattices in $PU (1, 1)$ , and more generally of fundamental groups of orientable...

Harmonie Forms Dual to Geodesic Cycles in Quotients of SU (p, 1).

Y.L. Tong, S.P. Wang (1981)

Mathematische Annalen

Hermitian curvature flow

Jeffrey Streets, Gang Tian (2011)

Journal of the European Mathematical Society

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...

Higher degree Galois covers of ${ℂℙ}^{1} \times T$ .

Amram, Meirav, Goldberg, David (2004)

Algebraic & Geometric Topology

Hölder continuity of solutions to the Monge-Ampère equations on compact Kähler manifolds

Pham Hoang Hiep (2010)

Annales de l’institut Fourier

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 $ω_{u}^{n}$ is moderate if $u$ is Hölder continuous. We prove a theorem which is a partial converse to this result.

Hölder continuous solutions to Monge–Ampère equations

Jean-Pierre Demailly, Sławomir Dinew, Vincent Guedj, Pham Hoang Hiep, Sławomir Kołodziej, Ahmed Zeriahi (2014)

Journal of the European Mathematical Society

Let $(X, ω)$ be a compact Kähler manifold. We obtain uniform Hölder regularity for solutions to the complex Monge-Ampère equation on $X$ with $L^{p}$ right hand side, $p > 1$ . The same regularity is furthermore proved on the ample locus in any big cohomology class. We also study the range $(X, ω)$ of the complex Monge-Ampère operator acting on $ω$ -plurisubharmonic Hölder continuous functions. We show that this set is convex, by sharpening Kołodziej’s result that measures with $L^{p}$ -density belong to $(X, ω)$ and proving that $(X, ω)$ has the...

Holomorphic Affine and Projective Connections of Hyperbolic Type.

Michael J. Markowitz (1979)

Mathematische Annalen

Holomorphic flows and complex structures on products of odd dimensional spheres.

Jean Jaques Loeb, Marcel Nicolau (1996)

Mathematische Annalen

Holomorphic line bundles and divisors on a domain of a Stein manifold

Makoto Abe (2007)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

Let $D$ be an open set of a Stein manifold $X$ of dimension $n$ such that $H^{k} (D, 𝒪) = 0$ for $2 \leq k \leq n - 1$ . We prove that $D$ is Stein if and only if every topologically trivial holomorphic line bundle $L$ on $D$ is associated to some Cartier divisor $𝔡$ on $D$ .

Holomorphic Maps of Compact Riemann Surfaces Into 2-Dimensional Compact C-Hyperbolic Manifolds.

Yoichi Imayoshi (1985)

Mathematische Annalen

Holomorphic Poisson Cohomology

Zhuo Chen, Daniele Grandini, Yat-Sun Poon (2015)

Complex Manifolds

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

Page 1 Next

Displaying 1 – 20 of 26

Harder-Narasimhan filtrations and optimal destabilizing vectors in complex geometry

Harmonic maps and representations of non-uniform lattices of $PU (m, 1)$

Harmonie Forms Dual to Geodesic Cycles in Quotients of SU (p, 1).

Hermitian curvature flow

Higher degree Galois covers of ${ℂℙ}^{1} \times T$ .

Hölder continuity of solutions to the Monge-Ampère equations on compact Kähler manifolds

Hölder continuous solutions to Monge–Ampère equations

Holomorphic Affine and Projective Connections of Hyperbolic Type.

Holomorphic flows and complex structures on products of odd dimensional spheres.

Holomorphic line bundles and divisors on a domain of a Stein manifold

Holomorphic Maps of Compact Riemann Surfaces Into 2-Dimensional Compact C-Hyperbolic Manifolds.

Holomorphic Poisson Cohomology

Holomorphic structures and connections on differentiable fibre bundles.

Holomorphic Vector Fields with Simple Isolated Zeros.

Holomorphy angles and sectional curvature in Hermitian elliptic planes over fields and tensor products of fields.

Homogeneous $C R$ -hypersurface-structures on spheres

Homotopie in homogenen komplexen Mannigfaltigkeiten.

Hyperbolic geometry on noncommutative balls.

Hyperbolically Imbedded Spaces and the Big Picard Theorem.

Hyperbolicity and branched coverings.

Currently displaying 1 – 20 of 26