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
Generating Pragmatic Examples to Train Neural Program SynthesizersUsing neural networks is a novel way to amortize a synthesizer’s…
2022
CLIP-Forge: Towards Zero-Shot Text-to-Shape GenerationGenerating shapes using natural language can enable new ways of…
2019
JOIN: an integrated platform for joint simulation of occupant-building interactionsSeveral approaches exist for simulating building properties (e…
2012
An optimization approach for extracting and encoding consistent maps in a shape collectionWe introduce a novel approach for computing high quality…
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