Luc Nguyen

collaborators

4 papers

math.AP2026

Cartan's and Gauss's equations and rigidity theorems for isometric embeddings in low Sobolev regularity

Isaac Newell, Luc Nguyen

Let ${I^\cdot^{i}}_{i = 1}^{2}$ be a an orthonormal coframe on a domain $U$ on a smooth surface $(I^£, g)$ . When $I^\cdot^{i}$ is smooth, it is well-known that there is a unique connection 1-form $Ï…

math.AP2026

Properties of hypersurface singular sets of solutions to the $I ¨ _{k}$ -Yamabe equation in the negative cone

Jonah A. J. Duncan, Luc Nguyen

We consider conformally flat Lipschitz viscosity solutions to the $I ¨ _{k}$ -Yamabe equation in the negative cone which admit smooth hypersurface singularities. Under natural regularit…

math.AP2025

The $I ¨ _{k}$ -Loewner-Nirenberg problem on Riemannian manifolds for $k = \frac{n}{2}$ and beyond

Jonah A. J. Duncan, Luc Nguyen

Let $(M^{n}, g_{0})$ be a smooth compact Riemannian manifold of dimension $n \geq 3$ with smooth non-empty boundary $\partial M$ . Let $I^ \subset R^{n}$ be a symmetric convex cone a…

math.AP2025

The fully nonlinear Loewner-Nirenberg problem: Liouville theorems and counterexamples to local boundary estimates

Jonah A. J. Duncan, Luc Nguyen

In this paper we give a complete classification of positive viscosity solutions $w$ to conformally invariant equations of the form \begin{align}\label{ab}\tag{ $*$ } \begin{cases} f(…

Cartan's and Gauss's equations and rigidity theorems for isometric embeddings in low Sobolev regularity

Properties of hypersurface singular sets of solutions to the I¨k​-Yamabe equation in the negative cone

The I¨k​-Loewner-Nirenberg problem on Riemannian manifolds for k=2n​ and beyond

The fully nonlinear Loewner-Nirenberg problem: Liouville theorems and counterexamples to local boundary estimates

Properties of hypersurface singular sets of solutions to the $I ¨ _{k}$ -Yamabe equation in the negative cone

The $I ¨ _{k}$ -Loewner-Nirenberg problem on Riemannian manifolds for $k = \frac{n}{2}$ and beyond