Special Lagrangian submanifolds of log Calabi-Yau manifolds
type: Item
instance of: scholarly article
title: Special Lagrangian submanifolds of log Calabi-Yau manifolds
zbMATH Open document ID: 1479.14046
DOI: 10.1215/00127094-2021-0012
author: Tristan C. Collins
author: Adam Jacob
author: Yu-Shen Lin
published in: Duke Mathematical Journal
publication date: 2021-07-08T00:00:00Z
full work available at URL: https://arxiv.org/abs/1904.08363
review text: The authors prove that if \(X\) is a Tian-Yau manifold and if the compact Calabi-Yau manifold at infinity admits a single special Lagrangian, then \(X\) admits infinitely many disjoint special Lagrangians. They effectively obtain resolutions of some conjectures of Auroux. They also apply their result to mirror symmetry for del Pezzo surfaces and rational elliptic surfaces.
reviewed by: Vehbi Emrah Paksoy
Mathematics Subject Classification ID: 14J32
Mathematics Subject Classification ID: 32Q25
Mathematics Subject Classification ID: 53D37
Mathematics Subject Classification ID: 53E10
zbMATH DE Number: 7369853
zbMATH Keywords: del Pezzo surface
zbMATH Keywords: Lagrangian mean curvature flow
zbMATH Keywords: mirror symmetry
zbMATH Keywords: rational elliptic surface
zbMATH Keywords: special Lagrangian
MaRDI profile type: Publication
OpenAlex ID: W3156374218
arXiv ID: 1904.08363
cites work: Q5593095
cites work: Mirror symmetry and T-duality in the complement of an anticanonical divisor
cites work: Special Lagrangian fibrations, mirror symmetry and Calabi-Yau double covers
cites work: Special Lagrangian fibrations, wall-crossing, and mirror symmetry
cites work: A Beginner’s Introduction to Fukaya Categories
cites work: Mirror symmetry for Del Pezzo surfaces: Vanishing cycles and coherent sheaves
cites work: A generalization of the isoperimetric inequality
cites work: Real analyticity of solutions of Hamilton's equation
cites work: Q5749404
cites work: Categorial mirror symmetry for K3 surfaces
cites work: Quantum Cohomology Rings of Toric Manifolds
cites work: Dual Polyhedra and Mirror Symmetry for Calabi-Yau Hypersurfaces in Toric Varieties
cites work: Laplacians and Riemannian submersions with totally geodesic fibres
cites work: On the spectrum of Riemannian submersions with totally geodesic fibers
cites work: Q5842038
cites work: Mirror symmetry on K3 surfaces as a hyper-Kähler rotation
cites work: Some examples of special Lagrangian tori
cites work: A pair of Calabi-Yau manifolds as an exactly soluble superconformal theory.
cites work: Stability of Kähler-Ricci flow
cites work: Q4830311
cites work: Enriques surfaces. I
cites work: Q4237088
cites work: Numerical characterization of the Kähler cone of a compact Kähler manifold
cites work: Q5439814
cites work: Mirror symmetry, Tyurin degenerations and fibrations on Calabi-Yau manifolds
cites work: Mirror symmetry for lattice polarized del Pezzo surfaces
cites work: Regularity theory for mean curvature flow
cites work: Complex analytic geometry
cites work: Morse theory for Lagrangian intersections
cites work: Algebraic surfaces and holomorphic vector bundles
cites work: Q4865995
cites work: Equivariant Gromov - Witten Invariants
cites work: A mirror theorem for toric complete intersections
cites work: Calibrated fibrations on noncompact manifolds via group actions
cites work: Analytische Faserungen über holomorph-vollständigen Räumen
cites work: Pseudo holomorphic curves in symplectic manifolds
cites work: Q4550191
cites work: Mirror symmetry for log Calabi-Yau surfaces. I
cites work: Theta functions and mirror symmetry
cites work: Collapsing of abelian fibered Calabi-Yau manifolds
cites work: Gromov-Hausdorff collapsing of Calabi-Yau manifolds
cites work: Large complex structure limits of \(K3\) surfaces
cites work: Sur La Classification Des Fibres Holomorphes Sur La Sphere de Riemann
cites work: Lectures on moduli spaces of elliptic curves
cites work: Asymptotically cylindrical Calabi-Yau manifolds
cites work: Gravitational instantons from rational elliptic surfaces
cites work: Calabi-Yau manifolds with isolated conical singularities
cites work: The moduli space of complex Lagrangian submanifolds
cites work: Q5702529
cites work: Bogomolov-Tian-Todorov theorems for Landau-Ginzburg models
cites work: A special Lagrangian \(3\)-torus as a real slice
cites work: On compact analytic surfaces. III
cites work: Homological Algebra of Mirror Symmetry
cites work: Twin Lagrangian fibrations in mirror symmetry

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cites work: Q3078257

Special Lagrangian submanifolds of log Calabi-Yau manifolds (cites work)
cites work: From special Lagrangian to Hermitian-Yang-Mills via Fourier-Mukai transform.

Special Lagrangian submanifolds of log Calabi-Yau manifolds (cites work)
cites work: Convergence of Lagrangian mean curvature flow in Kähler-Einstein manifolds

Special Lagrangian submanifolds of log Calabi-Yau manifolds (cites work)
cites work: Mean curvature flow in a Ricci flow background

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cites work: Landau-Ginzburg Hodge numbers for mirrors of del Pezzo surfaces

Special Lagrangian submanifolds of log Calabi-Yau manifolds (cites work)
cites work: \(J\)-holomorphic curves and symplectic topology

Special Lagrangian submanifolds of log Calabi-Yau manifolds (cites work)
cites work: Deformations of calibrated submanifolds

Special Lagrangian submanifolds of log Calabi-Yau manifolds (cites work)
cites work: Dynamics on blowups of the projective plane

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cites work: Q4000367

Special Lagrangian submanifolds of log Calabi-Yau manifolds (cites work)
cites work: The isoperimetric inequality

Special Lagrangian submanifolds of log Calabi-Yau manifolds (cites work)
cites work: Das Riemann-Hilbertsche Problem der Theorie der linearen Differentialgleichungen

Special Lagrangian submanifolds of log Calabi-Yau manifolds (cites work)
cites work: Q4550198

Special Lagrangian submanifolds of log Calabi-Yau manifolds (cites work)
cites work: Lagrangian torus fibration of quintic Calabi-Yau hypersurfaces. III. Symplectic topological SYZ mirror construction for general quintics.

Special Lagrangian submanifolds of log Calabi-Yau manifolds (cites work)
cites work: The existence of minimal immersions of 2-spheres

Special Lagrangian submanifolds of log Calabi-Yau manifolds (cites work)
cites work: The Geometries of 3-Manifolds

Special Lagrangian submanifolds of log Calabi-Yau manifolds (cites work)
cites work: Q4549289

Special Lagrangian submanifolds of log Calabi-Yau manifolds (cites work)
cites work: Deforming the metric on complete Riemannian manifolds

Special Lagrangian submanifolds of log Calabi-Yau manifolds (cites work)
cites work: Ricci deformation of the metric on complete non-compact Riemannian manifolds

Special Lagrangian submanifolds of log Calabi-Yau manifolds (cites work)
cites work: Holomorphic curves in symplectic geometry

Special Lagrangian submanifolds of log Calabi-Yau manifolds (cites work)
cites work: Angle theorems for the Lagrangian mean curvature flow

Special Lagrangian submanifolds of log Calabi-Yau manifolds (cites work)
cites work: Locality in the Fukaya category of a hyperkähler manifold

Special Lagrangian submanifolds of log Calabi-Yau manifolds (cites work)
cites work: Mirror symmetry is \(T\)-duality

Special Lagrangian submanifolds of log Calabi-Yau manifolds (cites work)
cites work: Q3472803

Special Lagrangian submanifolds of log Calabi-Yau manifolds (cites work)
cites work: Complete Kahler Manifolds with Zero Ricci Curvature. I

Special Lagrangian submanifolds of log Calabi-Yau manifolds (cites work)
cites work: Complete Kähler manifolds with zero Ricci curvature. II

Special Lagrangian submanifolds of log Calabi-Yau manifolds (cites work)
cites work: Limits of Calabi-Yau metrics when the Kähler class degenerates

Special Lagrangian submanifolds of log Calabi-Yau manifolds (cites work)
cites work: Adiabatic limits of Ricci-flat Kähler metrics

Special Lagrangian submanifolds of log Calabi-Yau manifolds (cites work)
cites work: Collapsing hyperkähler manifolds

Special Lagrangian submanifolds of log Calabi-Yau manifolds (cites work)
cites work: Harmonic functions on complete riemannian manifolds

Special Lagrangian submanifolds of log Calabi-Yau manifolds (cites work)
cites work: On the ricci curvature of a compact kähler manifold and the complex monge-ampére equation, I

Special Lagrangian submanifolds of log Calabi-Yau manifolds (cites work)
cites work: Gromov's Compactness Theorem for Pseudo Holomorphic Curves

Special Lagrangian submanifolds of log Calabi-Yau manifolds (cites work)
cites work: Torus fibrations of Calabi-Yau hypersurfaces in toric varieties