Dung The Tran

collaborators

4 papers

math.CO2026

Additive structures imply more distances in $F_{q}^{d}$

Daewoong Cheong, Gennian Ge, Doowon Koh +3

For a set $E \subseteq F_{q}^{d}$ , the distance set is defined as $I^ (E) := {∥ x - y ∥ : x, y \in E}$ , where $∥ \cdot ∥$ denotes the stan…

math.OC2026

Existence of Quantum Splines via Fourth-Order Gradient Flows

Chun-Chi Lin, Yang-Kai Lue, Dung The Tran

We establish a rigorous existence theory for the quantum splines introduced by Brody, Holm, and Meier in Physical Review Letters (2012). These curves arise as solutions of a variat…

math.CO2026

A functional Loomis-Whitney type inequality in the Heisenberg group and projection theorems over finite fields

Daewoong Cheong, Thang Pham, Dung The Tran

We establish functional Loomis--Whitney type inequalities in the finite Heisenberg group $H^{n} (F_{q})$ . For $n = 1$ , we determine the sharp region of exponents $(u_1,u…

math.OC2025

Higher-order Riemannian spline interpolation problems: a unified approach by gradient flows

Chun-Chi Lin, Dung The Tran

This paper addresses the problems of spline interpolation on smooth Riemannian manifolds, with or without the inclusion of least-squares fitting. Our unified approach utilizes grad…

Additive structures imply more distances in Fqd​

Existence of Quantum Splines via Fourth-Order Gradient Flows

A functional Loomis-Whitney type inequality in the Heisenberg group and projection theorems over finite fields

Higher-order Riemannian spline interpolation problems: a unified approach by gradient flows

Additive structures imply more distances in $F_{q}^{d}$