Qi Sun

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20242026

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math.DG2026

Singularities of Curve Shortening Flow with Convex Projections

Qi Sun

We show that any smooth closed immersed curve in $R^{n}$ with a one-to-one convex projection onto some $2$ -plane develops a Type~I singularity and becomes asymptotically circ…

math.DG2025

Huisken's Distance Comparison Principle in Higher Codimension

Qi Sun

We establish a variant of Huisken's distance comparison principle for reflection symmetric immersed Curve Shortening flow in $R^{n}, n \geq 2$ . As an application, we show that c…

math.DG2024

Curve Shortening Flow of Space Curves with Convex Projections

Qi Sun

We show that under Space Curve Shortening flow any closed immersed curve in $R^{n}$ whose projection onto $R^{2} \times {0}$ is convex remains smooth until it sh…