Yixin He

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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 CarathÃ©odory class

Yixin He, Quanyu Tang, Teng Zhang

We determine the optimal universal growth scale for the integral means of normalized logarithmic derivatives in the CarathÃ©odory 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 $\frac{I ^ » _{D_{1} \cap D_{2}} ( z )}{I ^ » _{D_{1}} ( z ) + I ^ » _{D_{2}} ( z )} .$ We solve a…

math.CV2026

Generalizing the Clunie--Hayman construction in an ErdÅs 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 $I^¼ (r, f) := max_{n \geq 0} ∣ a_{n} ∣ r^{n}$ . A problem of ErdÅs asks for the va…

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

Optimal universal growth for integral means of normalized logarithmic derivatives in the CarathÃ©odory class

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

On Fuchs's additive intersection problem for the hyperbolic metric

Generalizing the Clunie--Hayman construction in an ErdÅs maximum-term problem

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