A. Vogiatzi

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20232026

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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 $S^{n + m}$ , $m \geq 2$ , which generalises Pu's work on the convergence of submanifolds in $\mathbb{S…

math.DG2023

High Codimension Mean Curvature Flow in the Complex Projective Space

Artemis A. Vogiatzi

We study the mean curvature flow of smooth, compact submanifolds of high codimension with quadratic pinching in $C P^{k}$ . We establish a codimension estimate, where in regio…

math.DG2023

Singularity Models for High Codimension Mean Curvature Flow in Riemannian Manifolds

Artemis A. Vogiatzi, Huy T. Nguyen

We study the mean curvature flow of smooth $n$ -dimensional compact submanifolds with quadratic pinching in a Riemannian manifold $N^{n + m}$ . Our main focus is on the case…