منابع مشابه
Special Lagrangian Cones
We study homogeneous special Lagrangian cones in C with isolated singularities. Our main result constructs an infinite family of special Lagrangian cones in C 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 C with a spherical link – any such cone must be a plane. We also construct a one-par...
متن کاملSpecial Lagrangian Cones with Higher Genus Links
For every odd natural number g = 2d+1 we prove the existence of a countably infinite family of special Lagrangian cones in C over a closed Riemann surface of genus g, using a geometric PDE gluing method.
متن کاملSpecial Lagrangian cones in C³ and primitive harmonic maps
In this article I show that every special Lagrangian cone in C determines, and is determined by, a primitive harmonic surface in the 6symmetric space SU3/SO2. For cones over tori, this allows us to use the classification theory of harmonic tori to describe the construction of all the corresponding special Lagrangian cones. A parameter count is given for the space of these, and some of the examp...
متن کاملThe Geometric Complexity of Special Lagrangian T 2-cones
We prove a number of results on the geometric complexity of special Lagrangian (SLG) T -cones in C. Every SLG T -cone has a fundamental integer invariant, its spectral curve genus. We prove that the spectral curve genus of an SLG T -cone gives a lower bound for its geometric complexity, i.e. the area, the stability index and the Legendrian index of any SLG T -cone are all bounded below by expli...
متن کاملLagrangian Cones in C
In this article I show that every special Lagrangian cone in C 3 determines, and is determined by, a primitive harmonic surface in the 6-symmetric space SU3/SO2. For cones over tori, this allows us to use the classification theory of harmonic tori to describe the construction of all the corresponding special Lagrangian cones. A parameter count is given for the space of these, and some of the ex...
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ژورنال
عنوان ژورنال: American Journal of Mathematics
سال: 2004
ISSN: 1080-6377
DOI: 10.1353/ajm.2004.0029