Gregory R. Chambers

collaborators

3 papers

math.AP2025

Mountain Pass Critical Points of the Volume Constrained Area Functional

Gregory R. Chambers, Jared Marx-Kuo

We construct mountain pass critical points of the perimeter functional on sets of fixed volume. For a generic metric, this gives rise to a smooth almost embedded hypersurface with…

math.DG2025

Diameter, Area, and Mean curvature

Gregory R. Chambers, Jared Marx-Kuo

In this note, we extend diameter bounds of Simon, Topping, and Wu--Zheng to submanifolds with boundary and (potentially non-compact) ambient manifolds with minor curvature restrict…

math.GT2022

On the square peg problem

Gregory R. Chambers

We show that if $γ$ is a Jordan curve in $R^{2}$ which is close to a $C^{2}$ Jordan curve $β$ in $R^{2}$ , then $γ$ contains an inscribed square. In particular, if $κ> 0…