2 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…