Holomorphic maps into almost Kähler manifolds with constrained energy density

Abstract

In this paper, we prove an isolation theorem for holomorphic and anti-holomorphic maps from a compact conformal semi-Kähler manifold with or without boundary to an almost Kähler manifold with constrained energy density, which extends the results of Gauchman and Glazebrook. At the same time, as an analogy of a theorem of Ilias and Shouman, the corresponding results are improved.