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.DG2024
Index, Intersections, and Multiplicity of Min-Max Geodesics
Jared Marx-Kuo, Lorenzo Sarnataro, Douglas Stryker
We prove upper bounds for the Morse index and number of intersections of min-max geodesics achieving the -widths of a closed surface. A key tool in our analysis is a proof that…