15 citations · 29 across the 28 of their papers we have counts for
34 papers
Compact Mean Curvature Flows from Non-Compact Initial Data
Theodora Bourni, Nathan Burns, Marcus Flook
We construct compact, embedded solutions to the mean curvature flow in that arise from various non-compact initial data and exist for a finite time.
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…
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…
On the Relation between Graph Ricci Curvature and Community Structure
Sathyanarayanan Rengaswami, Theodora Bourni, Vasileios Maroulas
The connection between curvature and topology is a very well-studied theme in the subject of differential geometry. By suitably defining curvature on networks, the study of this th…
Classification of Convex Ancient Solutions to Free Boundary Curve Shortening Flow in Convex Domains
Theodora Bourni, Nathan Burns, Spencer Catron
We classify convex ancient curve shortening flows with free boundary on general bounded convex domains.