5 papers · 1 filter
Ancient solutions to free boundary mean curvature flow
Theodora Bourni, Giada Franz
We establish rigidity results for ancient solutions to the free boundary mean curvature flow in manifolds with convex boundary. In particular, we show that any free boundary minima…
Unknottedness of free boundary minimal surfaces and self-shrinkers
Sabine Chu, Giada Franz
We study unknottedness for free boundary minimal surfaces in a three-dimensional Riemannian manifold with nonnegative Ricci curvature and strictly convex boundary, and for self-shr…
Genus one critical catenoid
Giada Franz, Daniel Ketover, Mario B. Schulz
We use variational methods to construct a free boundary minimal surface in the three-dimensional unit ball with genus one, two boundary components and prismatic symmetry. Key ingre…
Topological control for min-max free boundary minimal surfaces
Giada Franz, Mario B. Schulz
We establish general bounds on the topology of free boundary minimal surfaces obtained via min-max methods in compact, three-dimensional ambient manifolds with mean convex boundary…
Inequivalent complexity criteria for free boundary minimal surfaces
Alessandro Carlotto, Giada Franz
We obtain a series of results in the global theory of free boundary minimal surfaces, which in particular provide a rather complete picture for the way different complexity criteri…