On stable minimal disks in manifolds with nonnegative isotropic curvature

摘要

Let N be a compact domain with weakly two-convex boundary ?N in a Riemannian 4-manifold M with nonnegative isotropic curvature. If D is a stable minimal disk in N with ?D ? ?N that solves the free boundary problem, then D is infinitesimally holomorphic; moreover, it is ± holomorphic if M is a K?hler surface with positive scalar curvature, and it is holomorphic for some complex structure if M is a hyperk?hler surface. We also show that if N is a compact domain in M of dimM ≧ 4 with nonnegative isotropic curvature and ?N is two-convex, then π_1(?N) → π_1(N) is injective.