5 citations · 6 across the 5 of their papers we have counts for
10 papers
Area comparison results for isotropic surfaces
Edward Goldstein
Consider a 2-plane and let be a bounded region in with a piecewise-smooth boundary. Let be the infimum of areas of all piecewise-smooth isot…
Volume minimization and estimates for certain isotropic submanifolds in complex projective spaces
Edward Goldstein
In this note we show the following result using the integral-geometric formula of R. Howard: Consider the totally geodesic in . Then it minimizes…
Some estimates related to Oh's conjecture for the Clifford tori in CP^n
Edward Goldstein
This note is motivated by Y.G. Oh's conjecture that the Clifford torus in minimizes volume in its Hamiltonian deformation class. We show that there exist expl…
A note on mean curvature, Maslov class and symplectic area of Lagrangian immersions
Kai Cieliebak, Edward Goldstein
In this note we prove a simple relation between the mean curvature form, symplectic area, and the Maslov class of a Lagrangian immersion in a Kähler-Einstein manifold. An immediate…
Volume minimization for Lagrangian submanifolds in complex manifolds with negative first Chern class
Edward Goldstein
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 g…
Holomorphic vector fields and minimal Lagrangian submanifolds
Edward Goldstein
The purpose of this note is to establish the following theorem: Let N be a Kahler manifold, L be a compact oriented immersed minimal Lagrangian submanifold in N and V be a holomorp…