Yixin He

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math.CV2026

A counterexample to Nevanlinna's century-old half-plane problem

Yixin He, Teng Zhang

Let $H = {z \in C : Im z > 0}$ , and let $N (H)$ denote the Nevanlinna class in $H$ , consisting of meromorphic functions representable as…

math.CV2026

Beurling--Carleson Endpoint Counterexamples: Singular Inner Functions and a Semilinear Equation

Pengcheng Fang, Yixin He

We settle two endpoint problems for Beurling--Carleson support conditions. For $0 < s < \frac{1}{2}$ and $θ = \frac{1 - 2 s}{1 - s}$ , we construct a nonatomic singular probability measure $μ$ , su…

math.CV2026

Optimal universal growth for integral means of normalized logarithmic derivatives in the Carathéodory class

Yixin He, Quanyu Tang, Teng Zhang

We determine the optimal universal growth scale for the integral means of normalized logarithmic derivatives in the Carathéodory class. This resolves a problem of D.~K.~Thomas.

math.CV2026

A Solution to a Problem of Rubel on Two-Parameter Normal Families of Entire Functions

Yixin He, Quanyu Tang, Teng Zhang

We construct an entire function $F (z, a, b) \in O (C^{3})$ such that the family ${F (\cdot, a, b) : a, b \in C}$ of entire functions of $z$ is normal on…

math.CV2026

On Fuchs's additive intersection problem for the hyperbolic metric

Yixin He, Quanyu Tang

For hyperbolic domains $D_{1}, D_{2} \subset {z \in C : ∣ z ∣ < R}$ and $z \in D_{1} \cap D_{2}$ , we consider the ratio $\frac{λ _{D_{1} \cap D_{2}} ( z )}{λ _{D_{1}} ( z ) + λ _{D_{2}} ( z )} .$ We solve a pr…

math.CV2026

Generalizing the Clunie--Hayman construction in an Erdős maximum-term problem

Yixin He, Quanyu Tang

Let $f (z) = \sum_{n \geq 0} a_{n} z^{n}$ be a transcendental entire function and write $M (r, f) := max_{∣ z ∣ = r} ∣ f (z) ∣$ and $μ (r, f) := max_{n \geq 0} ∣ a_{n} ∣ r^{n}$ . A problem of Erdős asks for the valu…