Year: 2026
Type: article
Abstract: We study the mean curvature flow of smooth, compact submanifolds of high codimension with quadratic pinching in $$\mathbb {C}P^k$$ C P k . We establish a codimension estimate, where in regions of high curvature, the submanifold becomes approximately codimension one, in a quantifiable way. Under a cylindrical type pinching, this limiting flow is weakly convex and moves by translation or is a self shrinker. These estimates allow us to analyse the behaviour of the flow near singularities and establish the existence of the limiting flow. With a decay estimate, the rescaling converges smoothly to a totally geodesic limit in infinite time, without using Stampacchia iteration or integral analysis.
Source: Journal of Geometric Analysis
Author: Artemis A. Vogiatzi
Institution: Queen Mary University of London
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,290
OpenAlex ID: W7126155331