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arxiv: math/0103045 · v1 · pith:V2IKHLMZnew · submitted 2001-03-07 · 🧮 math.CV · math.DG

Interpolation in non-positively curved K\"ahler manifolds

classification 🧮 math.CV math.DG
keywords ahlerinterpolationberndtssoncomparisonconditionsconnectedcurvaturecurved
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We extend to any simply connected K\"ahler manifold with non-positive sectional curvature some conditions for interpolation in $\mathbb{C}$ and in the unit disk given by Berndtsson, Ortega-Cerd\`a and Seip. The main tool is a comparison theorem for the Hessian in K\"ahler geometry due to Greene, Wu and Siu, Yau.

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