33 citations · 71 across the 17 of their papers we have counts for
16 papers · 1 filter
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 be a bounded smooth horoconvex domain and let be its first Dirichlet eigenfunction. We prove that \[ \operatorname{Hess}_{\mathbb H^2}(-\logψ_1)>0…
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…
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 , and prove that the product of the fundamental gap…
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…
The fundamental gap of horoconvex domains in
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…
The vanishing of the fundamental gap of convex domains in
Theodora Bourni, Julie Clutterbuck, Xuan Hien Nguyen +3
For the Laplace operator with Dirichlet boundary conditions on convex domains in , , we prove that the product of the fundamental gap with the square of the d…
Ancient solutions for flow by powers of the curvature in
Theodora Bourni, Julie Clutterbuck, Xuan Hien Nguyen +3
We construct a new compact convex embedded ancient solution of the flow in , that lies between two parallel lines. Using this solution we class…
Explicit fundamental gap estimates for some convex domains in
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 , showing that for some of them $λ_2 - λ_1 < \fra…
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…
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…
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 , for which the mean curvature flow behaves differently from the heat flow. In the first example, the two flo…
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…
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…
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…
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…
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…