Author

Teng-Ren Zhang

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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

Preprint Jul 2026

Sharp tangent inequalities in noncommutative $L_p$-spaces

Let $\mathcal{M}$ be a von Neumann algebra equipped with a faithful normal semifinite weight, and let $L_p(\mathcal{M})$ denote the associated Haagerup noncommutative $L_p$-space. For $1<p<\infty$, let $q=p/(p-1)$. For $z\in L_q(\mathcal{M})$ and $y\in L_p(\mathcal{M})$, denote by $\langle z,y\rangle=\operatorname{Re}\...

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