Volume minimization for Lagrangian submanifolds in complex manifolds with negative first Chern class

Details Volume minimization for Lagrangian submanifolds in complex manifolds with negative first Chern class Volume minimization for Lagrangian submanifolds in complex manifolds with negative first Chern class

2003-01-17

arxiv.org/abs/math/0301191v2

Mathematics

Differential Geometry

6 pages, minor modifications

Scientific paper

It is classically known that closed geodesics on a compact Riemann surface with a metric of negative curvature strictly minimize length in their free homotopy class. We'd like to generalize this to Lagrangian submanifolds in K\"ahler manifolds of negative Ricci curvature. The only known result in this direction is a theorem on Y.I. Lee for certain Lagrangian submanifolds in a product of two Riemann surfaces of constant negative curvature. We develop an approach to study this problem in higher dimensions. Along the way we prove some weak results (volume-minimization outside of a divisor) and give a counterexample to global volume-minimization for an immersed minimal Lagrangian submanifold.

Affiliated with

Also associated with

No associations

Rating

Volume minimization for Lagrangian submanifolds in complex manifolds with negative first Chern class does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Volume minimization for Lagrangian submanifolds in complex manifolds with negative first Chern class, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Volume minimization for Lagrangian submanifolds in complex manifolds with negative first Chern class will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-646557