Nathan Burns

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math.DG2026

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 $R^{n + 1}$ that arise from various non-compact initial data and exist for a finite time.

math.DG2026

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 $R^{2}$ which converges in finite time to a round half-point.

math.DG2024

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.