23 citations · 24 across the 8 of their papers we have counts for
10 papers
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…
On the stability of minimal submanifolds in conformal spheres
Giada Franz, Federico Trinca
Given an -dimensional Riemannian sphere conformal to the round one and -pinched, we show that it does not contain any closed stable minimal submanifold of dimension $2\le k\l…
Contributions to the theory of free boundary minimal surfaces
Giada Franz
In this thesis, we present various contributions to the study of free boundary minimal surfaces. After introducing some basic tools and discussing some delicate aspects related to…
Estimating the Morse index of free boundary minimal hypersurfaces through covering arguments
Santiago Cordero-Misteli, Giada Franz
Given a compact Riemannian manifold, of dimension between 3 and 7, with boundary, we adapt Song's method in Song (2023) to the free boundary case to show that the Morse index of a…
Equivariant index bound for min-max free boundary minimal surfaces
Giada Franz
Given a three-dimensional Riemannian manifold with boundary and a finite group of orientation-preserving isometries of this manifold, we prove that the equivariant index of a free…
Free boundary minimal surfaces with connected boundary and arbitrary genus
Alessandro Carlotto, Giada Franz, Mario B. Schulz
We employ min-max techniques to show that the unit ball in contains embedded free boundary minimal surfaces with connected boundary and arbitrary genus.
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…