Convexity of complements of limit sets for holomorphic foliations on surfaces

Bertrand Deroin, Christophe Dupont, Victor Kleptsyn

Let $\mathcal{F}$ be a holomorphic foliation on a compact Káhler surface with hyperbolic singularities and no foliation cycle. We prove that if the limit set of $\mathcal{F}$ has zer…