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Abstract
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 Kähler surface with positive scalar curvature, and it is holomorphic for some complex structure if M is a hyperkähler surface. We also show that if N is a compact domain in M of dim M ≧ 4 with nonnegative isotropic curvature and ∂N is two-convex, then π1(∂N) → π1(N) is injective.
Received: 2007-11-14
Published Online: 2010-06-21
Published in Print: 2010-June
© Walter de Gruyter Berlin · New York 2010
