Jonah A. J. Duncan

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20222024

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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

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…