arXiv subjects

Shuhui He

Publications and source records attributed to Shuhui He.

2 recordsLinked to original sources

arXiv2025

A curvature flow approach to dorsal closure modelling

In this paper we propose and study a curvature-based mathematical model for dorsal closure in embryonic drosophila. Using an analysis that mixes maximum-principle and integral-estimates, we establish global existence and convergence for data that mimics the initial geometry of a dorsal closure event. Further, we present a numerical approximation scheme for the flow, establishing stability, consistence, and convergence. We also give sample simulations of the flow with initial configurations that include experimentally observed data.

math.AP↗

arXiv2018

On a curvature flow model for embryonic epidermal wound healing

The paper studies a curvature flow linked to the physical phenomenon of wound closure. Under the flow we show that a closed, initially convex or close-to-convex curve shrinks to a round point in finite time. We also study the singularity, showing that the singularity profile after continuous rescaling is that of a circle. We additionally give a maximal time estimate, with an application to the classification of blowups.

math.DG↗