Paul Sweeney

activity

20232026

collaborators

5 papers

math.DG2026

Topology of tame contractible $n$ -manifolds, $n = 6, 7$ , with Positive BiRicci Curvature and Ricci lower bounds

Paul Sweeney

We show that if an open smooth $6$ -manifold $M^{6}$ is the interior of a compact, contractible manifold with boundary $X^{6}$ , such that $π_{3} (X, \partial X) = 0$ , and $M$ supports a compl…

math.DG2025

Positive curvature conditions on contractible manifolds

Paul Sweeney

Our goal is to identify curvature conditions that distinguish Euclidean space in the case of open, contractible manifolds and the disk in the case of compact, contractible manifold…

math.DG2024

Width Stability of Rotationally Symmetric Metrics

Hunter Stufflebeam, Paul Sweeney

We prove a conjecture of Marques-Neves in arXiv:2103.10093, and several alternative formulations thereof, about the stability of the min-max width of three-spheres under the additi…

math.DG2024

A Smooth Intrinsic Flat Limit of with Negative Curvature

Jared Krandel, Paul Sweeney

In 2014, Gromov asked if nonnegative scalar curvature is preserved under intrinsic flat convergence. Here we construct a sequence of closed oriented Riemannian $n$ -manifolds, $n\ge…

math.DG2023

Examples for Scalar Sphere Stability

Paul Sweeney

The rigidity theorems of Llarull and Marques-Neves, which show two different ways scalar curvature can characterize the sphere, have associated stability conjectures. Here we produ…

Topology of tame contractible n-manifolds, n=6,7, with Positive BiRicci Curvature and Ricci lower bounds

Positive curvature conditions on contractible manifolds

Width Stability of Rotationally Symmetric Metrics

A Smooth Intrinsic Flat Limit of with Negative Curvature

Examples for Scalar Sphere Stability

Topology of tame contractible $n$ -manifolds, $n = 6, 7$ , with Positive BiRicci Curvature and Ricci lower bounds