Interpolation in non-positively curved K\"ahler manifolds

Christophe Mourougane

doi:10.1007/BF02931003

Interpolation in non-positively curved K\"ahler manifolds

Complex Variables 2018-05-24 v1 Differential Geometry

Authors: Christophe Mourougane

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Abstract

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.

Keywords

interpolation Kähler manifolds non-positive curvature Hessian comparison theorem unit disk

Cite

@article{arxiv.math/0103045,
  title  = {Interpolation in non-positively curved K\"ahler manifolds},
  author = {Christophe Mourougane},
  journal= {arXiv preprint arXiv:math/0103045},
  year   = {2018}
}

Comments

9 pages, Latex

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