Author

Alexandre Eremenko

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Preprint Sep 2026

Holomorphic curves of finite lower order with few inflection points

We prove a conjecture proposed by the first-named author in 1998. Let $f\colon\mathbb{C}\to\mathbb{P}^n$ be a transcendental linearly non-degenerate holomorphic curve of finite lower order. If the counting function $N_1(r,f)$ of its Wronskian zeros satisfies $N_1(r,f)=o(T(r,f))$, then its order and lower order coincide...

Alexandre Eremenko, Zhang Teng · 0 citations

Preprint Sep 2026

The modified Cartan conjecture

In 1928 H. Cartan stated a conjecture about holomorphic curves in $\mathbb{P}^n$ parametrized by the unit disc, omitting $n+2$ hyperplanes in general position. He proved it for $n=2$. In 1996 the first-named author constructed counterexamples for all $n\geq 3$, and proposed a modified form of Cartan's conjecture which...

Alexandre Eremenko, Zong-Ben Xu, Teng-Ren Zhang · 0 citations