X. Han

activity

20242026

collaborators

4 papers

math.GT2026

Nearly geodesic surfaces are filling

Xiaolong Hans Han

Let $M$ be a closed hyperbolic $3$ -manifold. A homotopy class $[S]$ of surfaces in $M$ is filling if any representative cuts $M$ into components contractible in $M$ . We prove that…

math.PR2025

A few observations around Gaussian domination and continuous symmetry breaking for spin O(N) model

Xiao Han

We investigate the notion of Gaussian domination for the spin $O (N)$ model on general finite graphs. We begin by proving a general inequality for spin correlations under the assump…

math.CO2025

A new bound for the Fourier-Entropy-Influence conjecture

Xiao Han

In this paper, we prove that the Fourier entropy of an $n$ -dimensional boolean function $f$ can be upper-bounded by $O (I (f) + k \in [n] \sum I_{k} (f) lo g \frac{1}{I _{k} ( f )})$ , whe…

math.CA2024

Semiclassical measure of the spherical harmonics by Bourgain on $S^{3}$

Xiaolong Han

Bourgain used the Rudin-Shapiro sequences to construct a basis of uniformly bounded holomorphic functions on the unit sphere in $C^{2}$ . They are also spherical harmonics (i…

Nearly geodesic surfaces are filling

A few observations around Gaussian domination and continuous symmetry breaking for spin O(N) model

A new bound for the Fourier-Entropy-Influence conjecture

Semiclassical measure of the spherical harmonics by Bourgain on S3

Semiclassical measure of the spherical harmonics by Bourgain on $S^{3}$