Papers Published
Abstract:
Let SO(n) act in the standard way on C^n and extend this action in the usual
way to C^{n+1}. It is shown that nonsingular special Lagrangian submanifold
L in C^{n+1} that is invariant under this SO(n)-action intersects the fixed line
C in a nonsingular real-analytic arc A (that may be empty). If n>2, then A has
no compact component. Conversely, an embedded, noncompact nonsingular
real-analytic arc A in C lies in an embedded nonsingular special Lagrangian
submanifold that is SO(n)-invariant. The same existence result holds for
compact A if n=2. If A is connected, there exist n distinct nonsingular SO(n)-
invariant special Lagrangian extensions of A such that any embedded
nonsingular SO(n)-invariant special Lagrangian extension of A agrees with
one of these n extensions in some open neighborhood of A. The method
employed is an analysis of a singular nonlinear PDE and ultimately calls on
the work of Gerard and Tahara to prove the existence of the extension.
Keywords:
calibrations, special Lagrangian submanifolds