187 citations · 209 across the 11 of their papers we have counts for
11 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…
Geometric Model for Complex Non-Kaehler Manifolds with SU(3) Structure
Edward Goldstein, Sergey Prokushkin
For a given complex n-fold M we present an explicit construction of all complex (n+1)-folds which are principal holomorphic T2-fibrations over M. For physical applications we consi…