7 papers · 1 filter
Improved Index and Intersection bounds for Min-Max Geodesics
Lorenzo Sarnataro, Douglas Stryker, Jared Marx-Kuo
In this note, we show that the sum of the Morse index and number of intersections of min-max geodesics achieving the p-widths of a closed surface are bounded above by , improvin…
Boundary behaviour of stable Allen-Cahn limit-interfaces in Riemannian manifolds
Martin Man-chun Li, Davide Parise, Lorenzo Sarnataro
This is the second paper in our series of works to develop the min-max theory for free boundary minimal hypersurfaces in Riemannian manifolds with boundary via the Allen-Cahn equat…
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…
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…
Boundary behavior of limit-interfaces for the Allen-Cahn equation on Riemannian manifolds with Neumann boundary condition
Martin Li, Davide Parise, Lorenzo Sarnataro
We study the boundary behavior of any limit-interface arising from a sequence of general critical points of the Allen-Cahn energy functionals on a smooth bounded domain. Given any…
Existence of closed embedded curves of constant curvature via min-max
Lorenzo Sarnataro, Douglas Stryker
We find conditions under which Almgren-Pitts min-max for the prescribed geodesic curvature functional in a closed oriented Riemannian surface produces a closed embedded curve of co…
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…