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The fractional mean curvature flow
Bruno Pini Mathematical Analysis Seminar, 2020 In this note, we present some recent results in the study of the fractional mean curvature flow, that is a geometric evolution of the boundary of a set whose speed is given by the fractional mean curvature.
Eleonora Cinti
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Pinched hypersurfaces are compact
Advanced Nonlinear Studies, 2023 We make rigorous and old idea of using mean curvature flow to prove a theorem of Richard Hamilton on the compactness of proper hypersurfaces with pinched, bounded curvature.
Bourni Theodora +2 more
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Non-Parametric Mean Curvature Flow with Prescribed Contact Angle in Riemannian Products
Analysis and Geometry in Metric Spaces, 2022 Assuming that there exists a translating soliton u∞ with speed C in a domain Ω and with prescribed contact angle on ∂Ω, we prove that a graphical solution to the mean curvature flow with the same prescribed contact angle converges to u∞ + Ct as t →∞.
Casteras Jean-Baptiste +3 more
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Curvature-based interface restoration algorithm using phase-field equations.
PLoS ONE, 2023 In this study, we propose a restoration algorithm for distorted objects using a curvature-driven flow. First, we capture the convex-hull shaped contour of the distorted object using the mean curvature flow.
Seunggyu Lee, Yongho Choi
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Life-Span of Classical Solutions to Hyperbolic Inverse Mean Curvature Flow
Discrete Dynamics in Nature and Society, 2020 In this paper, we investigate the life-span of classical solutions to hyperbolic inverse mean curvature flow. Under the condition that the curve can be expressed in the form of a graph, we derive a hyperbolic Monge–Ampère equation which can be reduced to
Zenggui Wang
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Multi-Reconstruction from Points Cloud by Using a Modified Vector-Valued Allen–Cahn Equation
Mathematics, 2021 The Poisson surface reconstruction algorithm has become a very popular tool of reconstruction from point clouds. If we reconstruct each region separately in the process of multi-reconstruction, then the reconstructed objects may overlap with each other ...
Jin Wang, Zhengyuan Shi
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A remark on soliton equation of mean curvature flow
Anais da Academia Brasileira de Ciências, 2004 In this note, we consider self-similar immersions of the mean curvature flow and show that a graph solution of the soliton equation, provided it has bounded derivative, converges smoothly to a function which has some special properties (see Theorem 1.1 ...
Li Ma, Yang Yang
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Universality in mean curvature flow neckpinches [PDF]
, 2014 We study noncompact surfaces evolving by mean curvature flow. Without any symmetry assumptions, we prove that any solution that is $C^3$-close at some time to a standard neck will develop a neckpinch singularity in finite time, will become asymptotically
Gang, Zhou, Knopf, Dan
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Forced hyperbolic mean curvature flow [PDF]
, 2012 In this paper, we investigate two hyperbolic flows obtained by adding forcing terms in direction of the position vector to the hyperbolic mean curvature flows in \cite{klw,hdl}.
Mao, Jing
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A survey on Inverse mean curvature flow in ROSSes
Complex Manifolds, 2017 In this survey we discuss the evolution by inverse mean curvature flow of star-shaped mean convex hypersurfaces in non-compact rank one symmetric spaces.
Pipoli Giuseppe
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