A variational characterization of complex submanifolds

DOI10.1007/s00208-015-1322-9zbMath1359.53056OpenAlexW2236322694MaRDI QIDQ330844

Jun Sun, Claudio Arezzo

Publication date: 26 October 2016

Published in: Mathematische Annalen (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00208-015-1322-9

zbMATH Keywords

Kähler-Einstein surfacescalar curvaturearea functionalhomology classinteger currentprinciple symbolspace of immersions

Mathematics Subject Classification ID

Symplectic manifolds (general theory) (53D05) Global differential geometry of Hermitian and Kählerian manifolds (53C55) Geometric measure and integration theory, integral and normal currents in optimization (49Q15) Manifolds of mappings (58D15)

Related Items

The existence of \(J\)-holomorphic curves in almost Hermitian manifolds ⋮ \(L_p\)-functional and \(J\)-holomorphic curves in Kähler manifolds ⋮ A variational characterization of calibrated submanifolds ⋮ Variational characterizations of invariant submanifolds in Sasaki manifolds

Cites Work

• Unnamed Item
• Regularity of area minimizing currents. II: Center manifold
• Regularity of area minimizing currents. III: Blow-up
• Regularity of area minimizing currents I: gradient \(L^p\) estimates
• Minimal two spheres in Kähler-Einstein Fano manifolds
• A variational characterization of \(J\)-holomorphic curves
• On a set of polarized Kähler metrics on algebraic manifolds
• Symplectic critical surfaces in Kähler surfaces
• The second variation of area of minimal surfaces in four-manifolds
• Scalar curvature and projective embeddings. I
• Minimal surfaces in flat tori
• On stable currents and their application to global problems in real and complex geometry
• A characterization of holomorphic chains
• The second variation of the functional \(L\) of symplectic critical surfaces in Kähler surfaces
• The singular set of 1-1 integral currents
• Area minimizers in a \(K3\) surface and holomorphicity
• Minimal Surfaces by Moving Frames
• Holomorphic chains and the support hypothesis conjecture
• Nearly Kählerian embeddings of symplectic manifolds