Yixuan Pang

activity

20232026

collaborators

7 papers

math.CA2026

The Kakeya problem for codimension-two planes in $R^{n}$

Chun-Kit Lai, Yixuan Pang, Rahul Sethi +1

We study the $(n - 2)$ -plane Kakeya problem in $R^{n}$ ( $n \geq 4$ ) subject to convex Wolff axioms. In other words, we study finite families of $δ$ -neighborhoods of $(n - 2)$ -plan…

math.CA2026

Weighted mixed-norm estimates for circular averages and exceptional set estimates for the wave equation

Yixuan Pang, Chenjian Wang

We prove mixed-norm estimates for circular averages with respect to $α$ -dimensional fractal measures on $R^{2}$ , using circle tangency bounds when $α \in (0, 1]$ and a $δ$ -dis…

math.CA2025

A weighted formulation of refined decoupling and inequalities of Mizohata-Takeuchi-type for the moment curve

Anthony Carbery, Zane Kun Li, Yixuan Pang +1

Let $Γ$ be a compact patch of a well-curved $C^{n + 1}$ curve in $R^{n}$ with induced Lebesgue measure $d λ$ , and let $g \mapsto g d λ$ be the Fourier e…

math.CA2025

Weighted $L^{2}$ restriction and comparison of nondegeneracy conditions for quadratic manifolds of arbitrary codimensions

Zhenbin Cao, Jingyue Li, Changxing Miao +1

We systematically study weighted $L^{2}$ restriction for quadratic manifolds of arbitrary codimensions by sharp uniform Fourier decay estimates and a refinement of the Du-Zhang metho…

math.CA2024

Sharp restriction estimates for some degenerate higher codimensional quadratic surfaces

Zhenbin Cao, Changxing Miao, Yixuan Pang

The Fourier restriction conjecture is a fundamental problem in harmonic analysis. In this paper, we investigate restriction estimates for degenerate higher codimensional quadratic…

math.CA2024

A study guide for the $ℓ^{2}$ decoupling theorem for the paraboloid

Ataleshvara Bhargava, Tiklung Chan, Zi Li Lim +1

This article serves as a study guide for the $ℓ^{2}$ decoupling theorem for the paraboloid originally proved by Bourgain and Demeter. Given its popularity and importance, many exp…

math.CA2023

A short proof of an identity related to Type IV superorthogonality

Yixuan Pang

We provide a much shorter but even more powerful proof of an algebraic identity, which can be used to establish the direct and the converse inequality under Type IV superorthogonal…