Luc Nguyen · wovepaper

activity

20222026

most citedThe

σ_{k}

-Loewner-Nirenberg problem on Riemannian manifolds for

k < \frac{n}{2}

2 citations · 2 across the 6 of their papers we have counts for

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6 papers · 1 filter

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

Isaac Newell, Luc Nguyen

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

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

Jonah A. J. Duncan, Luc Nguyen

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

The $σ_{k}$ -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 $Γ \subset R^{n}$ be a symmetric convex cone an…

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(…

math.AP2023★ 2 cited

The $σ_{k}$ -Loewner-Nirenberg problem on Riemannian manifolds for $k < \frac{n}{2}$

Jonah A. J. Duncan, Luc Nguyen

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

Differential inclusions for the Schouten tensor and nonlinear eigenvalue problems in conformal geometry

Jonah A. J. Duncan, Luc Nguyen

Let $g_{0}$ be a smooth Riemannian metric on a closed manifold $M^{n}$ of dimension $n \geq 3$ . We study the existence of a smooth metric $g$ conformal to $g_{0}$ whose Schouten tensor $A…