Special Lagrangian cones

By M. Haskins. 2000

122 citations recorded by the source corpus.

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.

View Paper: https://www.semanticscholar.org/paper/4bce1a6e72d2177053e8d1f1743038a191204409

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

1. M. Haskins
2. H. Anciaux
3. D. Joyce
4. N. Kapouleas
5. I. McIntosh
6. I. Castro
7. Haizhong Li
8. F. Urbano

Citations in the corpus

• Special Lagrangian cones with higher genus links (2005, methodology): “The basic building blocks of our construction are provided by the U(1)-invariant SLG T 2 -cones constructed in [ 16 , 17] and described in Sect.”
• Lectures on special Lagrangian geometry (2001, background): “Many people have helped me develop my ideas on special Lagrangian geometry; amongst them I would particularly like to thank Robert Bryant, Mark Gross, Mark Haskins, Nigel Hitchin, Ian McIntosh, Richard Thomas, and Karen Uhlenbeck.”
• Special Lagrangian Cones in C3 and Primitive Harmonic Maps (2002, methodology): “We deduce (as did Haskins [12]) that there is a one-to-one correspondence between minimal Lagrangian (n+ 1)-cones in n+1 and minimal Legendrian n-folds in S2n+1.”
• Construction of Lagrangian Self-similar Solutions to the Mean Curvature Flow in $$\mathbb{C}^n$$ (2006, methodology): “The equation Im (γ n) = Const and its relations with special Lagrangian submanifolds was also considered independently in Haskins [15] and Joyce [16].”
• Special Lagrangian 3-folds and integrable systems (2001, background): “ C= −1, and two similar cases with B= 1 and C= 1, all of which give U(1)-invariant or R-invariant SL cones in C3 coming from the construction of [14, §8]. (See also Castro and Urbano [7], and Haskins [13].) 19 (b) Take B= 0 in Proposition 5.2. Then (35) shows that the phases δ1,δ2,δ3 are constant, s”
• HAMILTONIAN-MINIMAL LAGRANGIAN SUBMANIFOLDS IN COMPLEX SPACE FORMS (2004, methodology): “In particular, φ is minimal if and only if C(φ) is minimal; this result was used in [ H1 ] and [H2].”
• Special Lagrangian m-folds in ℂm with symmetries (2000, background): “This was first noticed by Castro and Urbano [2, Remark 1, p. 81– 2] in the context of minimal Lagrangian submanifolds, proved independently by Haskins [7, Th.”
• The geometric complexity of special Lagrangian T2-cones (2003, background): “We explain some consequences of our results for the programme (due to Joyce) to understand the “most common” three-dimensional isolated singularities of generic families of SLG submanifolds in almost Calabi-Yau manifolds.”