collaborators

6 papers

math.FA2026

Sharp Hardy inequalities for the Vladimirov--Taibleson operator on

Yaojia Sun

We prove sharp Hardy inequalities on for the quadratic form of the Vladimirov--Taibleson operator, the norm of its fractional derivative, and a nonlinear dif…

math.AP2026

Extension Problems for the Vladimirov--Taibleson Operator and the Hierarchical Laplacian

Yaojia Sun

We establish a non-Archimedean Caffarelli-Silvestre extension theory for the Vladimirov-Taibleson operator for and, more generally, for hierarchical Laplacians . F…

math.SP2026

Weyl's law and Pólya's conjecture for the Vladimirov-Taibleson operator

Yaojia Sun

This paper studies some fundamental problems in spectral geometry in the -adic setting. By viewing the Vladimirov-Taibleson operator as the -adic counterpart of the fra…

math.AP2026

Energy relations for the generalised Vladimirov derivative via Bruhat-Tits tree extensions

An Huang, Yaojia Sun

We formulate a proof on non-Archimedean analogue of the Caffarelli-Silvestre extension for fractional Laplacian on the Bruhat-Tits tree in terms of energy relations after ide…

math.NT2026

The Mean field equation on the Tate curve

Yaojia Sun

In this paper, we study the spectrum of the Laplacian on the Tate curve and construct the associated Green's function as a finite sum, which can be viewed as the non-Archimedean co…

math.NT2025

Green's function on the Tate curve

An Huang, Rebecca Rohrlich, Yaojia Sun +1

Motivated by the question of defining a -adic string worldsheet action in genus one, we define a Laplacian operator on the Tate curve, and study its Green's function. We show th…