Anisotropic area-preserving nonlocal flow for closed convex plane curves
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Tianyu Zhao
,
Yueyue Mao
Abstract
We consider an anisotropic area-preserving nonlocal flow for closed convex plane curves, which is a generalization of the model introduced by Pan and Yang (J. Differential Equations 266 (2019), 3764–3786) when τ = 1. Under this flow, the evolving curve maintains its convexity and converges to a homothety of a smooth symmetric strictly convex plane curve in the C∞ sense. The analysis of the asymptotic behavior of this flow implies the possibility of deforming one curve into another within the framework of Minkowski geometry.
Funding statement: The second author is supported by the Fundamental Research Funds for the Central Universities (Nos.3132023202, 3132022206). The fourth author is supported by the National Natural Science Foundation of China (No.11861004).
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Communicated by: T. Leistner
Acknowledgements
We express our gratitude to the anonymous referees for their diligent review of the original manuscript of this paper and for providing us with numerous invaluable comments.
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Articles in the same Issue
- Frontmatter
- Duality related with key varieties of ℚ-Fano threefolds constructed from projective bundles
- Continuous CM-regularity and generic vanishing
- Quotient spaces of K3 surfaces by non-symplectic involutions fixing a curve of genus 8 or more
- A note on polarized varieties with high nef value
- Anisotropic area-preserving nonlocal flow for closed convex plane curves
- New sextics of genus 6 and 10 attaining the Serre bound
- The balanced superelliptic mapping class groups are generated by three elements
- Bach flow of simply connected nilmanifolds
Articles in the same Issue
- Frontmatter
- Duality related with key varieties of ℚ-Fano threefolds constructed from projective bundles
- Continuous CM-regularity and generic vanishing
- Quotient spaces of K3 surfaces by non-symplectic involutions fixing a curve of genus 8 or more
- A note on polarized varieties with high nef value
- Anisotropic area-preserving nonlocal flow for closed convex plane curves
- New sextics of genus 6 and 10 attaining the Serre bound
- The balanced superelliptic mapping class groups are generated by three elements
- Bach flow of simply connected nilmanifolds
