X. H. Nguyen

activity

20062026

most citedComplete Embedded Self-Translating Surfaces under Mean Curvature Flow

33 citations · 71 across the 17 of their papers we have counts for

collaborators

21 papers

math.AP2026

Concavity of the Ornstein--Uhlenbeck torsion function on centered ellipses and its failure on convex domains

Xuan Hien Nguyen, Alina Stancu

Let $u$ be the torsion function of a bounded domain $Ω$ in $R^{n}$ for the Ornstein--Uhlenbeck operator, that is, the solution of $- Δ u + x \cdot \nabla u = 1$ in $Ω$ with $u=0…

math.AP2026

Failure of a Brunn-Minkowski-type inequality for the Gaussian torsional rigidity

Xuan Hien Nguyen, Alina Stancu

Let $u$ be the torsion function for the Ornstein-Uhlenbeck operator on a bounded domain $Ω \subset R^{n}$ , i.e., the solution of $Δ u - x \cdot \nabla u = - 1$ in $Ω$ with $u =…

math.DG2026

Log-Concavity and Level-Set Horoconvexity of the First Eigenfunction on Horoconvex Domains in the Hyperbolic Plane

Xianzhe Dai, John M. Ennis, Xuan Hien Nguyen +1

Let $Ω \subset H^{2}$ be a bounded smooth horoconvex domain and let $ψ_{1} > 0$ be its first Dirichlet eigenfunction. We prove that \[ \operatorname{Hess}_{\mathbb H^2}(-\logψ_1)>0…

math.DG2026

A Large-Diameter Fundamental-Gap Lower Bound for Horoconvex Domains

Xianzhe Dai, John Ennis, Xuan Hien Nguyen +1

We prove a large-diameter fundamental-gap lower bound for compact horoconvex domains in real hyperbolic space of curvature $-1$. The geometric part reduces large horoconvex domai…

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.DG2022

Log-Concavity and Fundamental Gaps on Surfaces of Positive Curvature

Gabriel Khan, Xuan Hien Nguyen, Malik Tuerkoen +1

We study the log-concavity of the first Dirichlet eigenfunction of the Laplacian for convex domains. For positively curved surfaces satisfying a condition involving the curvature a…

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…

math.DG2019

Explicit fundamental gap estimates for some convex domains in $H^{2}$

Theodora Bourni, Julie Clutterbuck, Xuan Hien Nguyen +3

Motivated by an example of Shih, we compute the fundamental gap of a family of convex domains in the hyperbolic plane $H^{2}$ , showing that for some of them $λ_2 - λ_1 < \fra…

math.DG2017

A survey of closed self-shrinkers with symmetry

Gregory Drugan, Hojoo Lee, Xuan Hien Nguyen

In this paper, we survey known results on closed self-shrinkers for mean curvature flow and discuss techniques used in recent constructions of closed self-shrinkers with classical…

math.DG2017

Shrinking doughnuts via variational methods

Gregory Drugan, Xuan Hien Nguyen

We use variational methods and a modified curvature flow to give an alternative proof of the existence of a self-shrinking torus under mean curvature flow. As a consequence of the…

math.DG2015

Mean curvature flow of an entire graph evolving away from the heat flow

Gregory Drugan, Xuan Hien Nguyen

We present two initial graphs over the entire $R^{n}$ , $n \geq 2$ for which the mean curvature flow behaves differently from the heat flow. In the first example, the two flo…

math.AP2015★ 6 cited

Finite topology self-translating surfaces for the mean curvature flow in $R^{3}$

Juan Dávila, Manuel del Pino, Xuan Hien Nguyen

Finite topology self translating surfaces to mean curvature flow of surfaces constitute a key element for the analysis of Type II singularities from a compact surface, since they a…

math.DG2012

Doubly periodic self-translating surfaces for the mean curvature flow

Xuan Hien Nguyen

We construct new examples of self-translating surfaces for the mean curvature flow from a periodic configuration with finitely many grim reaper cylinders in each period. Because th…

math.DG2011★ 31 cited

Construction of Complete Embedded Self-Similar Surfaces under Mean Curvature Flow. Part III

Xuan Hien Nguyen

We present new examples of complete embedded self-similar surfaces under mean curvature by gluing a sphere and a plane. These surfaces have finite genus and are the first examples…

math.DG2010★ 33 cited

Complete Embedded Self-Translating Surfaces under Mean Curvature Flow

Xuan Hien Nguyen

We describe a construction of complete embedded self-translating surfaces under mean curvature flow by desingularizing the intersection of a finite family of grim reapers in genera…

math.DG2007

Construction of Complete Embedded Self-Similar Surfaces under Mean Curvature Flow. Part II

Xuan Hien Nguyen

We study the Dirichlet problem associated to the equation for self-similar surfaces for graphs over the Euclidean plane with a disk removed. We show the existence of a solution pro…

math.DG2006★ 1 cited

Construction of Complete Embedded Self-Similar Surfaces under Mean Curvature Flow. Part I

Xuan Hien Nguyen

We carry out the first main step towards the construction of new examples of complete embedded self-similar surfaces under mean curvature flow. An approximate solution is obtained…

Concavity of the Ornstein--Uhlenbeck torsion function on centered ellipses and its failure on convex domains

Failure of a Brunn-Minkowski-type inequality for the Gaussian torsional rigidity

Log-Concavity and Level-Set Horoconvexity of the First Eigenfunction on Horoconvex Domains in the Hyperbolic Plane

A Large-Diameter Fundamental-Gap Lower Bound for Horoconvex Domains

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

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

Negative curvature constricts the fundamental gap of convex domains

Log-Concavity and Fundamental Gaps on Surfaces of Positive Curvature

The fundamental gap of horoconvex domains in Hn

The vanishing of the fundamental gap of convex domains in Hn

Ancient solutions for flow by powers of the curvature in R2

Explicit fundamental gap estimates for some convex domains in H2

A survey of closed self-shrinkers with symmetry

Shrinking doughnuts via variational methods

Mean curvature flow of an entire graph evolving away from the heat flow

Finite topology self-translating surfaces for the mean curvature flow in R3

Doubly periodic self-translating surfaces for the mean curvature flow

Construction of Complete Embedded Self-Similar Surfaces under Mean Curvature Flow. Part III

Complete Embedded Self-Translating Surfaces under Mean Curvature Flow

Construction of Complete Embedded Self-Similar Surfaces under Mean Curvature Flow. Part II

Construction of Complete Embedded Self-Similar Surfaces under Mean Curvature Flow. Part I

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

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

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

Explicit fundamental gap estimates for some convex domains in $H^{2}$

Finite topology self-translating surfaces for the mean curvature flow in $R^{3}$