On the compactness of Hamiltonian stationary Lagrangian surfaces in Kähler surfaces

DOI10.1007/s00526-020-01901-7zbMath1466.53088arXiv1910.02549OpenAlexW3148888725WikidataQ115386873 ScholiaQ115386873MaRDI QIDQ829515

John Man Shun Ma, Chen, Jingyi

Publication date: 6 May 2021

Published in: Calculus of Variations and Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1910.02549

zbMATH Keywords

Lagrangian toriLagrangian immersionWillmore energybubble tree convergence

Mathematics Subject Classification ID

Lagrangian submanifolds; Maslov index (53D12)

Related Items

Regularity of Hamiltonian stationary equations in symplectic manifolds ⋮ Regularity of critical points of the volume functional for Lagrangian submanifolds

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• \(W^{2,2}\)-conformal immersions of a closed Riemann surface into \(\mathbb{R}^n\)
• Hamiltonian stationary tori in Kähler manifolds
• The existence of Hamiltonian stationary Lagrangian tori in Kähler manifolds of any dimension
• The spectral data for Hamiltonian stationary Lagrangian tori in \(\mathbb R^4\)
• The classification of Hamiltonian stationary Lagrangian tori in \({{\mathbb {CP}}^2}\) by their spectral data
• Bubble tree convergence for harmonic maps
• Harmonic maps from degenerating Riemann surfaces
• The denominators of Lagrangian surfaces in complex Euclidean plane
• The existence of minimal immersions of 2-spheres
• Compactification of moduli space of harmonic mappings
• Volume minimization of Lagrangian submanifolds under Hamiltonian deformations
• Gromov's compactness theorem for pseudo-holomorphic curves
• Construction of many Hamiltonian stationary Lagrangian surfaces in Euclidean four-space
• Hamiltonian stationary Lagrangian surfaces in \(\mathbb{C}^2\)
• Minimizing area among Lagrangian surfaces: the mapping problem.
• On the regularity of Hamiltonian stationary Lagrangian submanifolds
• Construction of Hamiltonian-minimal Lagrangian submanifolds in complex Euclidean space
• The space of compact self-shrinking solutions to the Lagrangian mean curvature flow in \(\mathbb{C}^2\)
• Existence of surfaces minimizing the Willmore functional
• Hamiltonian stationary Lagrangian surfaces in \(\mathbb C \mathbb{P}^{2}\)
• Examples of Hamiltonian stationary Lagrangian tori in \(\mathbb CP^2\)
• Second variation and stabilities of minimal Lagrangian submanifolds in Kähler manifolds
• Bubble tree of branched conformal immersions and applications to the Willmore functional
• On the existence of Hamiltonian stationary Lagrangian submanifolds in symplectic manifolds
• Minimal Surfaces by Moving Frames
• Some regularity theorems in riemannian geometry
• Sur la géométrie des sous-fibrés et des feuilletages lagrangiens
• Submanifolds with Constant Mean Curvature
• Elliptic Partial Differential Equations of Second Order
• Lagrangian isometric immersions of a real-space-form Mⁿ(c) into a complex-space-form M˜ⁿ(4c)
• Extendability of Conformal Structures on Punctured Surfaces