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High Codimension Mean Curvature Flow in the Complex Projective Space
Open accessAbstract
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.
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References 23 · Cited by 4
Research works printed but not linked: 27
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Metadata
- Authors
- Vogiatzi, A. A.
- Affiliations
- Queen Mary University of London (GB)
- Corresponding author
- Vogiatzi, Artemis A.
- ORCID
- Vogiatzi, Artemis A.
- Venue
- The Journal of Geometric Analysis
- Published
- 2026-01-30
- Volume
- 36
- Issue
- 3
- ISSN
- 1050-6926 (ISSN-L)
- 1559-002X
- OpenAlex
- W4388327630
- Cited by
- 4
- References
- 23
- Citations by year
- 2026: 3
- FWCI
- 6.59
- Type
- journal article
- Language
- en
- Open access
- hybrid
- doi.org
- Licence
- cc-by
- creativecommons.org/licenses/by/4.0 (tdm)
- creativecommons.org/licenses/by/4.0 (vor)
- Locations
- Journal of Geometric Analysis (publishedVersion, cc-by)
- arXiv (Cornell University) (submittedVersion, cc-by)
- arXiv (Cornell University)
- Funders
- Copenhagen University
- Topics
- Physical Sciences › Mathematics › Applied Mathematics › Geometric Analysis and Curvature Flows
- Physical Sciences › Mathematics › Geometry and Topology › Advanced Differential Geometry Research
- Physical Sciences › Mathematics › Geometry and Topology › Geometry and complex manifolds
- Keywords
- mean curvature flow, complex projective space, singularities, rescaling, totally geodesic submanifolds, decay estimates, gradient estimates
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