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arXiv · 1911.06507

The CAT(0) geometry of convex domains with the Kobayashi metrics

Jinsong Liu·Hongyu Wang
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Abstract

Let $(\Omega,K_{\Omega})$ be a convex domain in $\mathbb C^d$ with the Kobayashi metric $K_{\Omega}$. In this paper we prove that $m$-convexity is a necessary condition for $(\Omega, K_{\Omega})$ to be CAT(0) if $d=2$. Moreover, when $\Omega \subset \mathbb{C}^d, \: d\geq3$, we obtain a similar result with the further smoothness assumption on its boundary.

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Jinsong Liu, Hongyu Wang. 2019-11-15. The CAT(0) geometry of convex domains with the Kobayashi metrics. https://arxiv.org/abs/1911.06507

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