The space of compact self-shrinking solutions to the Lagrangian mean curvature flow in \(\mathbb{C}^2\)

DOI10.1515/crelle-2015-0110zbMath1400.53053arXiv1406.6316OpenAlexW2952409049MaRDI QIDQ1789366

John Man Shun Ma, Chen, Jingyi

Publication date: 10 October 2018

Published in: Journal für die Reine und Angewandte Mathematik (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1406.6316

zbMATH Keywords

genusarea boundembedded torusbranched conformally immersed Lagrangian self-shrinker

Mathematics Subject Classification ID

Related Items (6)

On the compactness of Hamiltonian stationary Lagrangian surfaces in Kähler surfaces ⋮ Uniqueness of asymptotically conical higher codimension self-shrinkers and self-expanders ⋮ Remarks on the self-shrinking Clifford torus ⋮ Examples of equivariant Lagrangian mean curvature flow ⋮ Compactness and finiteness theorems for rotationally symmetric self shrinkers ⋮ Entropy bounds, compactness and finiteness theorems for embedded self-shrinkers with rotational symmetry

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• \(W^{2,2}\)-conformal immersions of a closed Riemann surface into \(\mathbb{R}^n\)
• Smooth compactness of self-shrinkers
• Bubble tree convergence for harmonic maps
• Asymptotic behavior for singularities of the mean curvature flow
• The space of minimal embeddings of a surface into a three-dimensional manifold of positive Ricci curvature
• The normalized curve shortening flow and homothetic solutions
• Pseudo holomorphic curves in symplectic manifolds
• The existence of minimal immersions of 2-spheres
• A new conformal invariant and its applications to the Willmore conjecture and the first eigenvalue of compact surfaces
• Compactification of moduli space of harmonic mappings
• Holomorphic curves in symplectic geometry
• Elliptic partial differential equations of second order
• The space of embedded minimal surfaces of fixed genus in a 3-manifold. IV: Locally simply connected
• Existence of surfaces minimizing the Willmore functional
• Compactness of the space of embedded minimal surfaces with free boundary in three-manifolds with nonnegative Ricci curvature and convex boundary
• The self-intersections of a smooth \(n\)-manifold in \(2n\)-space
• The Clifford Torus as a Self-Shrinker for the Lagrangian Mean Curvature Flow
• Bubble tree of branched conformal immersions and applications to the Willmore functional
• Minimal Immersions of Closed Riemann Surfaces
• Sur la géométrie des sous-fibrés et des feuilletages lagrangiens

This page was built for publication: The space of compact self-shrinking solutions to the Lagrangian mean curvature flow in \(\mathbb{C}^2\)