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.
2023
Challenges in Extracting Insights from Life Cycle Assessment Documents During Early Stage DesignKnowledge transfer from LCA documents and building a structured…
2012
Programming and Controlling Self-Folding RobotsThis paper describes a robot in the form of a self-folding sheet that…
2007
Dynamic 2D Patterns for Shading 3D ScenesWe describe a new way to render 3D scenes in a variety of…
2021
Meshmixer: Mesh Technology for Interactive Design and FabricationMeshmixer is a prototype design tool based on high-resolution dynamic…
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