In this lecture we will describe new results we have obtained on the problem of minimizing volume among Lagrangian submanifolds of Kdhler (or more generally symplectic) manifolds. We also provide motivation for this problem involving the construction of minimal lagrangian cycles in Kdhler-Einstein manifolds. For Calabi-Yau manifolds, this construction is a part of the mirror symmetry program.
Thu Feb 13 16:13:38 PST 1997