Publication
Deformations of minimal Lagrangian submanifolds with boundary
AbstractLet L be a special Lagrangian submanifold of a compact Calabi-Yau manifold M with boundary lying on the symplectic, codimension 2 submanifold W. It is shown how deformations of L which keep the boundary of L confined to W can be described by an elliptic boundary value problem, and two results about minimal Lagrangian submanifolds with boundary are derived using this fact. The first is that the space of minimal Lagrangian submanifolds near L with boundary on W is found to be finite dimensional and is parametrized over the space of harmonic 1-forms of L satisfying Neumann boundary conditions. The second is that if W’ is a symplectic, codimension 2 submanifold sufficiently near W, then, under suitable conditions, there exists a minimal Lagrangian submanifold L’ near L with boundary on W’.
Download publicationRelated Resources
See what’s new.
2007
Q&A: Jos Stam, Autodesk Principal Research ScientistAsk animators and VFX artists what was the most challenging part of…
2009
Analytic Drawing of 3D ScaffoldsWe describe a novel approach to inferring 3D curves from perspective…
2022
3D User Interfaces: Human Experience in 3D EnvironmentsDesigning user interfaces for interacting with 3D data involves a…
Get in touch
Something pique your interest? Get in touch if you’d like to learn more about Autodesk Research, our projects, people, and potential collaboration opportunities.
Contact us