Special Lagrangian cones
Copyright policy )Special Lagrangian cones
We study special Lagrangian cones in [inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="01i" /] with isolated singularities especially the case n = 3. Our main result constructs an infinite family of special Lagrangian cones in [inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="02i" /] each of which has a toroidal link. We obtain a detailed geometric description of these tori. We prove a regularity result for special Lagrangian cones in [inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="03i" /] with a spherical link—any such cone must be a plane. We also construct a one-parameter family of asymptotically conical special Lagrangian submanifolds from any special Lagrangian cone.
- Johns Hopkins University United States
Mathematics - Differential Geometry, Lagrangian cones, Differential geometric aspects of harmonic maps, harmonic maps, Legendrian immersions, 53C38 (Primary), 53C43 (Secondary), Calibrations and calibrated geometries, Lagrangian submanifolds; Maslov index, Differential Geometry (math.DG), Mathematics - Symplectic Geometry, FOS: Mathematics, Symplectic Geometry (math.SG), Harmonic maps, etc., singularities
Mathematics - Differential Geometry, Lagrangian cones, Differential geometric aspects of harmonic maps, harmonic maps, Legendrian immersions, 53C38 (Primary), 53C43 (Secondary), Calibrations and calibrated geometries, Lagrangian submanifolds; Maslov index, Differential Geometry (math.DG), Mathematics - Symplectic Geometry, FOS: Mathematics, Symplectic Geometry (math.SG), Harmonic maps, etc., singularities
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