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math.DG2026
High Codimension Curve Shortening Flow with Free Boundary
Huy The Nguyen, Artemis A. Vogiatzi
We study curve shortening flow in high codimension for arcs with free boundary meeting a fixed smooth barrier orthogonally. We prove dilation-invariant curvature and higher-derivat…
math.DG2024
Sharp Quartic Pinching for the Mean Curvature Flow in the Sphere
Artemis A. Vogiatzi
We prove a sharp quartic curvature pinching for the mean curvature flow in , , which generalises Pu's work on the convergence of submanifolds in $\mathbb{S…