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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…