Deformations of minimal Lagrangian submanifolds with boundary

Author:
Adrian Butscher

Journal:
Proc. Amer. Math. Soc. **131** (2003), 1953-1964

MSC (2000):
Primary 58J05

DOI:
https://doi.org/10.1090/S0002-9939-02-06800-4

Published electronically:
October 24, 2002

MathSciNet review:
1955286

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Abstract | References | Similar Articles | Additional Information

Abstract: Let be a special Lagrangian submanifold of a compact Calabi-Yau manifold with boundary lying on the symplectic, codimension 2 submanifold . It is shown how deformations of which keep the boundary of confined to 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 with boundary on is found to be finite dimensional and is parametrized over the space of harmonic 1-forms of satisfying Neumann boundary conditions. The second is that if is a symplectic, codimension 2 submanifold sufficiently near , then, under suitable conditions, there exists a minimal Lagrangian submanifold near with boundary on .

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Additional Information

**Adrian Butscher**

Affiliation:
Max Planck Institute for Gravitational Physics, am Muehlenberg 1, 14476 Golm Brandenburg, Germany

Address at time of publication:
Department of Mathematics, University of Toronto at Scarborough, Scarborough, Ontario, Canada M1C 1A4

Email:
butscher@aei-potsdam.mpg.de, butscher@utsc.utoronto.ca

DOI:
https://doi.org/10.1090/S0002-9939-02-06800-4

Received by editor(s):
October 11, 2001

Received by editor(s) in revised form:
January 24, 2002

Published electronically:
October 24, 2002

Communicated by:
Bennett Chow

Article copyright:
© Copyright 2002
American Mathematical Society