Minimal Lagrangian 2‐Tori in CP2 Come in Real Families of Every Dimension

By Emma Carberry, I. McIntosh. 2003

55 citations recorded by the source corpus.

It is shown that for every non‐negative integer n, there is a real n‐dimensional family of minimal Lagrangian tori in CP2, and hence of special Lagrangian cones in C3 whose link is a torus. The proof utilises the fact that such tori arise from integrable systems, and can be described using algebro‐geometric (spectral curve) data.

Subfields: Applied Mathematics, Geometry and Topology, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/213d5fdf3448ca1e8d54d5c90eba0aa1d33cc0de

How researchers see this paper

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

In Applied Mathematics

1. N. Kapouleas
2. M. Haskins
3. M. Li
4. S. Brendle
5. Peter J. McGrath
6. Iskander A. Taimanov
7. Dmitry Berdinsky

In Geometry and Topology

1. N. Kapouleas
2. M. Haskins
3. M. Li
4. S. Brendle
5. Peter J. McGrath
6. Iskander A. Taimanov
7. Dmitry Berdinsky

In Statistical and Nonlinear Physics

1. N. Kapouleas
2. M. Haskins

Citations in the corpus

• Special Lagrangian cones with higher genus links (2005, methodology): “f this construction is crucial to this paper. Very recently, the existence of many more SLG cones over 2-tori in S5 was proved using more sophisticated algebro-geometric tools from integrable systems [6,39]. Recent results [17, Thms. C & D] prove that these examples rapidly become geometrically ”
• The geometric complexity of special Lagrangian T2-cones (2003, background): “They arise as possible tangent cones to SLG currents at isolated singular points. Recently a number of authors have used integrable systems techniques to prove existence of large numbers of SLG cones [8,21,25,39]. Even in dimension three there are too many SLG cones to expect a complete classificatio”