Special Lagrangian cones with higher genus links

Abstract

For every odd natural number g=2d+1 we prove the existence of a countably infinite family of special Lagrangian cones in C^3 over a closed Riemann surface of genus g, using a geometric PDE gluing method.

48 pages

References in corpus (6)

• Mirror Symmetry is T-Duality
• Fivebranes, Membranes and Non-Perturbative String Theory
• Lectures on Special Lagrangian Submanifolds
• Special Lagrangian Fibrations I: Topology
• Special Lagrangian m-folds in C^m with symmetries
• The geometric complexity of special Lagrangian $T^2$-cones

Cited by in corpus (15)

• Free boundary minimal surfaces in the unit ball : recent advances and open questions
• Doubling and Desingularization Constructions for Minimal Surfaces
• Special Lagrangian conifolds, I: Moduli spaces
• Special Lagrangian conifolds, I: Moduli spaces (extended version)
• Minimal Lagrangian Surfaces in CH2 and Representations of Surface Groups into SU(2,1)
• Desingularization of Coassociative 4-folds with Conical Singularities: Obstructions and Applications
• Duality of Positive Currents and Plurisubharmonic Functions in Calibrated Geometry
• The Mean Curvature of Special Lagrangian 3-folds in SU(3)-Structures with Torsion
• Embedded Constant Mean Curvature Surfaces in Euclidean Three Space
• Some 3-dimensional transverse C-links (Constructions of higher-dimensional C-links, I)
• New examples of compact special Lagrangian submanifolds embedded in hyper-Kähler manifolds
• Hamiltonian stationary cones with isotropic links
• Equivariant Gluing Constructions of Contact Stationary Legendrian Submanifolds of the (2n+1)-Sphere
• Higher-order conservation laws for the non-linear Poisson equation via the characteristic cohomology
• Cayley cones ruled by 2-planes: desingularization and implications of the twistor fibration