Jonah A. J. Duncan

collaborators

5 papers

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.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

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…