Global solutions to the volume-preserving mean-curvature flow

DOI10.1007/s00526-015-0943-xzbMath1336.53082arXiv1502.07232OpenAlexW2105041263WikidataQ59470508 ScholiaQ59470508MaRDI QIDQ262200

Christian Seis, Luca Mugnai, Emanuele Nunzio Spadaro

Publication date: 29 March 2016

Published in: Calculus of Variations and Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1502.07232

zbMATH Keywords

global solutionsvolume constrainttime discretizationmean-curvature flowvolume preserving

Mathematics Subject Classification ID

Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Variational problems concerning minimal surfaces (problems in two independent variables) (58E12)

Related Items

Long time behavior of discrete volume preserving mean curvature flows, Diffusion-redistanciation schemes for 2D and 3D constrained Willmore flow: application to the equilibrium shapes of vesicles, Mass-conserving diffusion-based dynamics on graphs, Projection Method for Droplet Dynamics on Groove-Textured Surface with Merging and Splitting, Convergence of the thresholding scheme for multi-phase mean-curvature flow, Minimizing movements for mean curvature flow of droplets with prescribed contact angle, On volume-preserving crystalline mean curvature flow, Volume preserving mean curvature flow for star-shaped sets, Motion by crystalline-like mean curvature: A survey, Alexandrov's theorem revisited, The existence of a weak solution to volume preserving mean curvature flow in higher dimensions, The asymptotics of the area-preserving mean curvature and the Mullins-Sekerka flow in two dimensions, Asymptotic of the discrete volume-preserving fractional mean curvature flow via a nonlocal quantitative Alexandrov theorem, Weak-strong uniqueness for volume-preserving mean curvature flow, Nonlocal estimates for the volume preserving mean curvature flow and applications, Long time behaviour of the discrete volume preserving mean curvature flow in the flat torus, Quantitative Alexandrov theorem and asymptotic behavior of the volume preserving mean curvature flow, Consistency of the flat flow solution to the volume preserving mean curvature flow, Stationary sets of the mean curvature flow with a forcing term, Front propagation in the shadow wave-pinning model, Stationary sets and asymptotic behavior of the mean curvature flow with forcing in the plane, Minimizing movements for forced anisotropic mean curvature flow of partitions with mobilities, Implicit time discretization for the mean curvature flow of mean convex sets

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Convergence of a mass conserving Allen-Cahn equation whose Lagrange multiplier is nonlocal and local
• Volume-constrained minimizers for the prescribed curvature problem in periodic media
• Mass conserving Allen-Cahn equation and volume preserving mean curvature flow
• Volume preserving mean curvature flow of revolution hypersurfaces between two equidistants
• Nuovi teoremi relativi alle misure \((r - 1)\)-dimensionali in uno spazio ad \(r\) dimensioni
• The volume-preserving mean curvature flow in Euclidean space
• The volume preserving crystalline mean curvature flow of convex sets in \(\mathbb R^N\)
• Implicit time discretization for the mean curvature flow equation
• A simple scheme for volume-preserving motion by mean curvature
• Elliptic partial differential equations of second order
• A PDE-based fast local level set method
• Area-preserving curve-shortening flows: From phase separation to image processing
• Riemannian geometries on spaces of plane curves
• Sets of Finite Perimeter and Geometric Variational Problems
• Crossover in coarsening rates for the monopole approximation of the Mullins–Sekerka model with kinetic drag
• The volume preserving mean curvature flow.
• The volume preserving mean curvature flow near spheres
• Volume-Preserving Mean Curvature Flow as a Limit of a Nonlocal Ginzburg-Landau Equation
• Stefan and Hele-Shaw type models as asymptotic limits of the phase-field equations
• Volume preserving anisotropic mean curvature flow
• Curvature-Driven Flows: A Variational Approach
• On the Coarsening Rates for Attachment-Limited Kinetics
• Volume preserving mean curvature flow in the hyperbolic space