3 papers
math.DG2026
Existence of free boundary minimal disks in convex regions
Lorenzo Sarnataro, Douglas Stryker, Zhichao Wang +1
We show that any three-ball with mean convex boundary contains an embedded free boundary minimal disk. Moreover, when the three-ball is a strictly convex domain with nonnegative Ri…
math.DG2025
Optimal regularity for minimizers of the prescribed mean curvature functional over isotopies
Lorenzo Sarnataro, Douglas Stryker
We prove the optimal regularity for minimizers of the prescribed mean curvature functional over isotopy classes. As an application, we find an embedded sphere of prescrib…
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…