X. H. Nguyen

activity

20172025

collaborators

9 papers

math.AP2025

Constant potentials do not minimise the fundamental gap on convex domains in hyperbolic space

Julie Clutterbuck, Frieder Jäckel, Xuan Hien Nguyen

We show that for every $n \geq 2$ and $D > 0$ there exist a convex domain $Ω \subseteq H^{n}$ with diameter $D$ and a convex potential $V$ on $Ω$ such that the fundamental gap…

math.AP2025

Regularity of solutions to degenerate and singular free boundary problems with volume constraint

T. M. Nascimento, X. H. Nguyen, P. R. Stinga

We prove existence and regularity of solutions to degenerate and singular elliptic free boundary problems, where the volume of the positivity set of the solution is prescribed.

math.DG2022

Negative curvature constricts the fundamental gap of convex domains

Gabriel Khan, Xuan Hien Nguyen

We consider the Laplace-Beltrami operator with Dirichlet boundary conditions on convex domains in a Riemannian manifold $(M^{n}, g)$ , and prove that the product of the fundamental gap…

math.DG2021

The fundamental gap of horoconvex domains in $H^{n}$

Xuan Hien Nguyen, Alina Stancu, Guofang Wei

We show that, for horoconvex domains in the hyperbolic space, the product of their fundamental gap with the square of their diameter has no positive lower bound. The result follows…

math.DG2020

The vanishing of the fundamental gap of convex domains in $H^{n}$

Theodora Bourni, Julie Clutterbuck, Xuan Hien Nguyen +3

For the Laplace operator with Dirichlet boundary conditions on convex domains in $H^{n}$ , $n \geq 2$ , we prove that the product of the fundamental gap with the square of the d…

math.DG2020

Ancient solutions for flow by powers of the curvature in $R^{2}$

Theodora Bourni, Julie Clutterbuck, Xuan Hien Nguyen +3

We construct a new compact convex embedded ancient solution of the $κ^{α}$ flow in $R^{2}$ , $α \in (\frac{1}{2}, 1)$ that lies between two parallel lines. Using this solution we class…