\(L^2\) vanishing theorem on some Kähler manifolds

DOI10.1007/s11856-021-2092-6zbMath1468.53061arXiv1811.10772OpenAlexW3120428989MaRDI QIDQ2022775

Teng Huang

Publication date: 29 April 2021

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

Full work available at URL: https://arxiv.org/abs/1811.10772

zbMATH Keywords

Yang-Mills connectionHermitian vector bundleHermitian connection

Mathematics Subject Classification ID

Global differential geometry of Hermitian and Kählerian manifolds (53C55) Differential geometric aspects of harmonic maps (53C43) Relations of PDEs with special manifold structures (Riemannian, Finsler, etc.) (58J60) Vanishing theorems (32L20)

Related Items (2)

Vanishing theorem on parabolic Kähler manifolds ⋮ On \(L^2\)-harmonic forms of complete almost Kähler manifold

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• An \(L^2\)-isolation theorem for Yang-Mills fields on Kähler surfaces
• \(L^2\) harmonic forms on some complete Kähler manifolds
• The topology of asymptotically locally flat gravitational instantons
• On the anti-self-duality of the Yang-Mills connection over higher dimensional Kaehlerian manifold
• On complex analytic vector bundles
• Erratum: Moduli spaces of self-dual connections over asymptotically locally flat gravitational instantons
• Infinite dimensionality of the middle \(L^2\)-cohomology on non-compact Kähler hyperbolic manifolds
• The Chern classes of Sobolev connections
• The gap phenomena of Yang-Mills fields over the complete manifold
• \(L^2\)-cohomology of hyperkähler quotients
• Complex geometry. An introduction
• The cohomology of the space of magnetic monopoles
• An energy gap for Yang-Mills connections
• Vanishing theorems for \(L^2\)-cohomology on infinite coverings of compact Kähler manifolds and applications in algebraic geometry
• On the energy spectrum of Yang-Mills instantons over asymptotically locally flat spaces
• Kähler hyperbolicity and \(L_ 2\)-Hodge theory
• A special Stoke's theorem for complete Riemannian manifolds
• On Kähler varieties of restricted type. (An intrinsic characterization of algebraic varieties.)
• Non-self-dual Yang-Mills connections with nonzero Chern number
• Anti Self-Dual Yang-Mills Connections Over Complex Algebraic Surfaces and Stable Vector Bundles
• Solutions to Yang—Mills equations that are not self-dual
• Differential Analysis on Complex Manifolds
• A VANISHING THEOREM FOR L²COHOMOLOGY ON COMPLETE MANIFOLDS
• On the existence of hermitian-yang-mills connections in stable vector bundles
• On Cohomology Groups of Compact Analytic Varieties with Coefficients in Some Analytic Faisceaux
• On a Differential-Geometric Method in the Theory of Analytic Stacks
• Kähler parabolicity and the Euler number of compact manifolds of non-positive sectional curvature

This page was built for publication: \(L^2\) vanishing theorem on some Kähler manifolds