On an area-preserving inverse curvature flow of convex closed plane curves

Gao, Laiyuan; Pan, Shengliang; Tsai, De‐Hao

doi:10.1016/j.jfa.2021.108931

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2023

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Cited by 14 publications

(1 citation statement)

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“…Numerical computations in fact indicate that then a singularity appears for this initial curve, see Mayer [38]. For curves, it was also shown recently, that a star-shaped, centrosymmetric set keeps this properties and converges to a round sphere, see [22].…”

Section: Introductionmentioning

confidence: 77%

Nonlocal estimates for the Volume Preserving Mean Curvature Flow and applications

Lambert¹,

Mäder-Baumdicker²

2022

Preprint

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Section: Introductionmentioning

confidence: 77%

Nonlocal estimates for the Volume Preserving Mean Curvature Flow and applications

Lambert¹,

Mäder-Baumdicker²

2022

Preprint

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Nonlocal estimates for the volume preserving mean curvature flow and applications

Lambert¹,

Mäder-Baumdicker²

2023

Calc. Var.

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We obtain estimates on nonlocal quantities appearing in the volume preserving mean curvature flow (VPMCF) in the closed, Euclidean setting. As a result we demonstrate that blowups of finite time type I singularities of VPMCF are ancient solutions to mean curvature flow (MCF), prove that monotonicity methods may always be applied at these finite times and obtain information on the asymptotics of the flow. In the case of type II singularities, asymptotic flows corresponding to ’Hamilton’s rescaling procedures’ are eternal solutions of the MCF.

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Linear interpolation on $$k^{\alpha }$$-type area-preserving and length-preserving curve flows

Guo

Zhu

2022

Monatsh Math

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On an area-preserving inverse curvature flow of convex closed plane curves

Cited by 14 publications

References 21 publications

Nonlocal estimates for the Volume Preserving Mean Curvature Flow and applications

Nonlocal estimates for the Volume Preserving Mean Curvature Flow and applications

Nonlocal estimates for the volume preserving mean curvature flow and applications

Linear interpolation on $$k^{\alpha }$$-type area-preserving and length-preserving curve flows

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