Jonah A. J. Duncan

activity

20202026

most citedLocal pointwise second derivative estimates for strong solutions to the

σ_{k}

-Yamabe equation on Euclidean domains

5 citations · 7 across the 11 of their papers we have counts for

collaborators

11 papers

math.AP2026

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…

math.AP2025

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…

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(…

math.DG2024

The first Steklov eigenvalue on manifolds with nonnegative Ricci curvature and convex boundary

Jonah A. J. Duncan, Aditya Kumar

We establish a new lower bound for the first non-zero Steklov eigenvalue of a compact Riemannian manifold with non-negative Ricci curvature and (strictly) convex boundary. Related…

math.AP2024

Fully nonlinear Yamabe-type problems on non-compact manifolds

Jonah A. J. Duncan, Yi Wang

We obtain existence results for a class of fully nonlinear Yamabe-type problems on non-compact manifolds, addressing both the so-called positive and negative cases. We also give ex…

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…

math.DG2023

An improved eigenvalue estimate for embedded minimal hypersurfaces in the sphere

Jonah A. J. Duncan, Yannick Sire, Joel Spruck

Suppose that $Σ^{n} \subset S^{n + 1}$ is a closed embedded minimal hypersurface. We prove that the first non-zero eigenvalue $λ_{1}$ of the induced Laplace-Beltrami operator on $…

math.AP2023

Augmented Hessian equations on Riemannian manifolds: from integral to pointwise local second derivative estimates

Jonah A. J. Duncan

We obtain a priori local pointwise second derivative estimates for solutions $u$ to a class of augmented Hessian equations on Riemannian manifolds, in terms of the $C^{1}$ norm and c…

math.AP2022

Interior regularity for strong solutions to a class of fully nonlinear elliptic equations

Jonah A. J. Duncan

We obtain local pointwise second derivative estimates for $W^{2, p}$ -strong solutions to a class of fully nonlinear elliptic equations on Euclidean domains, motivated by problems in…

math.AP2022

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…

math.AP2020★ 5 cited

Local pointwise second derivative estimates for strong solutions to the $σ_{k}$ -Yamabe equation on Euclidean domains

Jonah A. J. Duncan, Luc Nguyen

We prove local pointwise second derivative estimates for positive $W^{2, p}$ solutions to the $σ_{k}$ -Yamabe equation on Euclidean domains, addressing both the positive and negative c…

Properties of hypersurface singular sets of solutions to the σk​-Yamabe equation in the negative cone

The σk​-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

The first Steklov eigenvalue on manifolds with nonnegative Ricci curvature and convex boundary

Fully nonlinear Yamabe-type problems on non-compact manifolds

The σk​-Loewner-Nirenberg problem on Riemannian manifolds for k<2n​

An improved eigenvalue estimate for embedded minimal hypersurfaces in the sphere

Augmented Hessian equations on Riemannian manifolds: from integral to pointwise local second derivative estimates

Interior regularity for strong solutions to a class of fully nonlinear elliptic equations

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

Local pointwise second derivative estimates for strong solutions to the σk​-Yamabe equation on Euclidean domains

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

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

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

Local pointwise second derivative estimates for strong solutions to the $σ_{k}$ -Yamabe equation on Euclidean domains