The asymptotics of the area-preserving mean curvature and the Mullins-Sekerka flow in two dimensions
DOI10.1007/s00208-022-02497-3arXiv2112.13936MaRDI QIDQ6084220
Vesa Julin, Emanuele Nunzio Spadaro, Massimiliano Morini, Marcello Ponsiglione
Publication date: 31 October 2023
Published in: Mathematische Annalen (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2112.13936
isoperimetric inequalityAlexandrov theoremminimizing movement schemeasymptotically exponential convergence rateincremental minimization problemtwo-phase flat torus Mullins-Sekerka flow
Multiphase and multicomponent flows (76T99) Variational methods applied to problems in fluid mechanics (76M30) Optimization of shapes other than minimal surfaces (49Q10) Inequalities and extremum problems in real or complex geometry (51M16)
Related Items (3)
Cites Work
- Unnamed Item
- Unnamed Item
- Global solutions to the volume-preserving mean-curvature flow
- Minimality via second variation for a nonlocal isoperimetric problem
- Isoperimetry with upper mean curvature bounds and sharp stability estimates
- The Hele--Shaw problem and area-preserving curve-shortening motions
- The volume preserving crystalline mean curvature flow of convex sets in \(\mathbb R^N\)
- Implicit time discretization for the mean curvature flow equation
- A center manifold analysis for the Mullins-Sekerka model
- Hypersurfaces with mean curvature given by an ambient Sobolev function.
- A sharp quantitative version of Alexandrov's theorem via the method of moving planes
- Bubbling with \(L^2\)-almost constant mean curvature and an Alexandrov-type theorem for crystals
- Convergence of the Cahn-Hilliard equation to the Hele-Shaw model
- Quantitative estimates for almost constant mean curvature hypersurfaces
- Stationary sets and asymptotic behavior of the mean curvature flow with forcing in the plane
- Long time behavior of discrete volume preserving mean curvature flows
- Volume preserving mean curvature flow for star-shaped sets
- Uniqueness of critical points of the anisotropic isoperimetric problem for finite perimeter sets
- Volume preserving mean curvature flows near strictly stable sets in flat torus
- Nonlinear stability results for the modified Mullins-Sekerka and the surface diffusion flow
- The sharp quantitative isoperimetric inequality
- Alexandrov's theorem revisited
- Some dynamic properties of volume preserving curvature driven flows
- Long time behaviour of the discrete volume preserving mean curvature flow in the flat torus
- A Singular Example for the Averaged Mean Curvature Flow
- Control of the isoperimetric deficit by the Willmore deficit
- Sets of Finite Perimeter and Geometric Variational Problems
- On the Shape of Compact Hypersurfaces with Almost-Constant Mean Curvature
- Integral Inequalities of Poincare and Wirtinger Type for BV Functions
- Solutions for the two-phase Stefan problem with the Gibbs–Thomson Law for the melting temperature
- Front migration in the nonlinear Cahn-Hilliard equation
- Stability in the Isoperimetric Problem
- The volume preserving mean curvature flow.
- A multi-phase Mullins–Sekerka system: matched asymptotic expansions and an implicit time discretisation for the geometric evolution problem
- The volume preserving mean curvature flow near spheres
- Curvature-Driven Flows: A Variational Approach
- On the Coarsening Rates for Attachment-Limited Kinetics
- Mullins-Sekerka as the Wasserstein flow of the perimeter
- Existence of Weak Solutions for the Mullins--Sekerka Flow
- Self-intersections for the surface diffusion and the volume-preserving mean curvature flow
- Weak-strong uniqueness for the mean curvature flow of double bubbles
- Stability analysis for stationary solutions of the Mullins–Sekerka flow with boundary contact
- Quantitative Alexandrov theorem and asymptotic behavior of the volume preserving mean curvature flow
This page was built for publication: The asymptotics of the area-preserving mean curvature and the Mullins-Sekerka flow in two dimensions
