4 papers
Aleksandrov reflection for Geometric Flows in Hyperbolic Spaces
Theodora Bourni, José M. Espinar, Aakash Mishra
We develop an Aleksandrov reflection framework for a large class of expanding curvature flows in hyperbolic space, with inverse mean curvature flow serving as a model case. The met…
Stability of the Shrinking Semi-Circle Under the Free Boundary Curve Shortening Flow
Theodora Bourni, Nathan Burns, Mat Langford
We establish a sharp rate of convergence for a free-boundary curve shortening flow in a convex domain in which converges in finite time to a round half-point.
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…
Ancient Ricci flows of bounded girth
Theodora Bourni, Timothy Buttsworth, Ramiro Lafuente +1
For each , we construct a 'pancake-like', -invariant ancient Ricci flow with positive curvature operator and bounded "girth", and we determine its asympt…