Properness for circle packings and Delaunay circle patterns on complex projective structures

Jean-Marc Schlenker; Andrew Yarmola

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arXiv · 1806.05254

Properness for circle packings and Delaunay circle patterns on complex projective structures

Jean-Marc Schlenker·Andrew Yarmola

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Abstract

We consider circle packings and, more generally, Delaunay circle patterns - arrangements of circles arising from a Delaunay decomposition of a finite set of points - on surfaces equipped with a complex projective structure. Motivated by a conjecture of Kojima, Mizushima and Tan, we prove that the forgetful map sending a complex projective structure admitting a circle packing with given nerve (resp. a Delaunay circle pattern with given nerve and intersection angles) to the underlying complex structure is proper.

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BibTeX RIS

Jean-Marc Schlenker, Andrew Yarmola. 2018-06-13. Properness for circle packings and Delaunay circle patterns on complex projective structures. https://arxiv.org/abs/1806.05254

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