John N. Treuer

activity

20192026

most citedRigidity theorem by the minimal point of the Bergman kernel

8 citations · 19 across the 11 of their papers we have counts for

collaborators

11 papers

math.CV2026

A new strong rigidity phenomenon for the Bergman metric

Peter Ebenfelt, John N. Treuer, Ming Xiao

We establish a new local-to-global rigidity phenomenon for the Bergman metric. Namely, under natural geometric hypotheses, a local conformal identification of Bergman metrics deter…

math.CV2025

The Levi $q$ -core and Property ( $P_{q}$ )

Gian Maria Dall'Ara, Samuele Mongodi, John N. Treuer

We introduce the Grassmannian $q$ -core of a distribution of subspaces of the tangent bundle of a smooth manifold. This is a generalization of the concept of the core previously int…

math.CV2025

Domains with Bergman metrics of constant curvature and Bergman-negligible subsets

Peter Ebenfelt, John N. Treuer, Ming Xiao

Let $D$ be a bounded domain in $C^{n}$ . Suppose the holomorphic sectional curvature of its Bergman metric equals a negative constant $τ$ . We show that $D$ is biholomorphic t…

math.CV2024

Rotational symmetries of domains and orthogonality relations

Soumya Ganguly, John N. Treuer

Let $Ω \subset C^{n}$ be a domain whose Bergman space contains all holomorphic monomials. We derive sufficient conditions for $Ω$ to be Reinhardt, complete Reinhardt, circula…

math.SP2024

Sharp decay rate for eigenfunctions of perturbed periodic Schrödinger operators

Wencai Liu, Rodrigo Matos, John N. Treuer

This paper investigates uniqueness results for perturbed periodic Schrödinger operators on $Z^{d}$ . Specifically, we consider operators of the form $H = - Δ + V + v$ , where $Δ…

math.CV2023

Modifications of the Levi core

Tanuj Gupta, Emil J. Straube, John N. Treuer

We construct a family of subdistributions of the Levi core $C (N)$ called modified Levi cores ${M C_{A}}_{A}$ indexed…

math.CV2022★ 1 cited

Sufficient condition for compactness of the $\partial$ -Neumann operator using the Levi core

John N. Treuer

On a smooth, bounded pseudoconvex domain $Ω$ in $C^{n}$ , to verify that Catlin's Property ( $P$ ) holds for $b Ω$ , it suffices to check that it holds on the set of D'Angelo inf…

math.CV2021★ 3 cited

Rigidity theorems by capacities and kernels

Robert Xin Dong, John N. Treuer, Yuan Zhang

For any open hyperbolic Riemann surface $X$ , the Bergman kernel $K$ , the logarithmic capacity $c_{β}$ , and the analytic capacity $c_{B}$ satisfy the inequality chain $πK \geq c^2_β \…

math.CV2021

Rigidity theorem of the Bergman kernel by analytic capacity

John Treuer

In [7], Dong and I proved that the domains $D \subset C$ of finite volume whose on-diagonal Bergman kernels $K (\cdot, \cdot)$ satisfy $K (z_{0}, z_{0}) = V o l u m e (D)^{- 1}$ are di…

math.CV2020★ 8 cited

Rigidity theorem by the minimal point of the Bergman kernel

Robert Xin Dong, John Treuer

We use the Suita conjecture (now a theorem) to prove that for any domain $Ω \subset C$ its Bergman kernel $K (\cdot, \cdot)$ satisfies $K (z_{0}, z_{0}) = Volume (Ω)^{- 1}$ …

math.CV2019★ 7 cited

Sharp pointwise and uniform estimates for $\partial ˉ$

Robert Xin Dong, Song-Ying Li, John N. Treuer

We use weighted $L^{2}$ -methods to obtain sharp pointwise estimates for the canonical solution to the equation $\partial ˉ u = f$ on smoothly bounded strictly convex domains and the…