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.
2024
Multidisciplinary Modular Approach to Kinematic Mechanism SynthesisWe present the first set of Mechanical Building Blocks modelled so…
2018
Hybrid Finite Element-Geometric Forming Simulation of Composite MaterialsComputer simulations can extensively help engineers to gain a better…
2012
Interactive Modeling with Mesh SurfacesIn the world of modern surface design tools, a mesh is simply a data…
2017
Annotation Graphs: A Graph-Based Visualization for Meta-Analysis of Data based on User-Authored AnnotationsUser-authored annotations of data can support analysts in the activity…
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