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math.DG2026
Free boundary minimal surfaces of genus zero
Otis Chodosh, Matilde Gianocca
We prove that any embedded genus zero free boundary minimal surface in the ball has first Steklov eigenvalue . This implies the uniqueness of the critical catenoid.
math.DG2026
No compromise in the liquid drop model
Otis Chodosh, Matilde Gianocca
We characterize minimizers in Gamow's liquid drop problem.
math.DG2026
Minimal hypersurfaces of Morse index one
Otis Chodosh, Matilde Gianocca
We prove that a complete, connected, embedded, minimal hypersurface in with finite total curvature and Morse index one is the higher-dimensional catenoid.