Positive forms on hyperkähler manifolds

zbMath1196.32011arXiv0801.1899MaRDI QIDQ987163

Misha Verbitsky

Publication date: 13 August 2010

Published in: Osaka Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0801.1899

zbMATH Keywords

hyper-Kähler manifoldshypercomplex manifoldsquaternionic Dolbeault complexquaternionic Hermitian structuresSibony's lemmaSkoda-El Mir theorem

Mathematics Subject Classification ID

Hyper-Kähler and quaternionic Kähler geometry, ``special geometry (53C26) Plurisubharmonic functions and generalizations (32U05) Other notions of convexity in relation to several complex variables (32F17)

Related Items

Existence of HKT metrics on hypercomplex manifolds of real dimension 8 ⋮ The \(C^0\) estimate for the quaternionic Calabi conjecture ⋮ On the Alesker-Verbitsky conjecture on hyperKähler manifolds ⋮ Weak solutions to the quaternionic Monge-Ampère equation ⋮ Subvarieties of hypercomplex manifolds with holonomy in \(SL(n,\mathbb H)\) ⋮ Hyperholomorphic connections on coherent sheaves and stability ⋮ Plurisubharmonic functions in calibrated geometry and \(q\)-convexity ⋮ Quaternionic Monge-Ampère equation and Calabi problem for HKT-manifolds

Cites Work

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• Sur le prolongement des courants positifs fermés
• Canonical bundles of complex nilmanifolds, with applications to hypercomplex geometry
• Quelques problèmes de prolongement de courants en analyse complexe
• Hyperkähler metrics and supersymmetry
• Vector bundles on complex projective spaces
• Prolongement des courants, positifs, fermes de masse finie
• Quaternionic complexes
• Hypercomplex varieties
• Hyperkähler manifolds with torsion obtained from hyperholomorphic bundles
• Geometry of hyper-Kähler connections with torsion
• Twistor spaces for hyper-Kähler manifolds with torsion
• Hyper-Kähler manifolds with torsion, supersymmetry and Hodge theory.
• Plurisubharmonic functions in calibrated geometry and \(q\)-convexity
• Plurisubharmonic functions on hypercomplex manifolds and HKT-geometry
• Potentials for hyper-Kähler metrics with torsion
• Sur les groupes d'holonomie homogènes de variétés à connexion affine et des variétés riemanniennes
• An introduction to potential theory in calibrated geometry
• Duality of positive currents and plurisubharmonic functions in calibrated geometry
• A Note on Hyperhermitian Four-Manifolds
• Métriques kählériennes et fibrés holomorphes
• On the ricci curvature of a compact kähler manifold and the complex monge-ampére equation, I
• On the existence of hermitian-yang-mills connections in stable vector bundles
• Yang-Mills fields on quaternionic spaces
• Quaternionic Dolbeault complex and vanishing theorems on hyperkähler manifolds