Paper · Dec 9, 2022
Minimizing Movements for Anisotropic and Inhomogeneous Mean Curvature Flows
As on arXiv
Abstract
In this paper we address anisotropic and inhomogeneous mean curvature flows with forcing and mobility, and show that the minimizing movements scheme converges to level set/viscosity solutions and to distributional solutions à la Luckhaus-Sturzenhecker to such flows, the latter holding in low dimension and conditionally to a convergence of the energies. By doing so we generalize recent works concerning the evolution by mean curvature by removing the hypothesis of translation invariance, which in the classical theory allows to simplify many arguments.
Its neighbourhood
Connected papers
The 8 papers on this site closest to this one, judged by the topics they share, the words and phrases in their titles and abstracts, and their authors. They are not its citations, but a map of the work around it. Papers here go back to 2021, plus the canon.
-
Minimizing movements for the generalized power mean curvature flow
Topics Weak & singular flows · Shared terms “minimizing movements”, “scheme converges”, “movement scheme”
-
Minimizing movements for forced anisotropic curvature flow of droplets
Topics Homogeneous spaces, Weak & singular flows · Shared terms “minimizing movements”, “inhomogeneous”
-
De Giorgi varifold solutions to Mean Curvature Flow: a minimizing movements approach
Topics Weak & singular flows · Shared terms “minimizing movements”, “Luckhaus Sturzenhecker”, “movement scheme”
-
Variational Nonlinear and Nonlocal Curvature Flows
Topics Weak & singular flows · Same author Daniele De Gennaro · Shared terms “minimizing movements”, “movement scheme”, “level set”
-
A convergence result for a minimizing movement scheme for mean curvature flow with prescribed contact angle in a curved domain
Topics Weak & singular flows · Shared terms “minimizing movements”, “movement scheme”, “scheme converges”
-
Generic level sets in mean curvature flow are BV solutions
Topics Weak & singular flows · Shared terms “viscosity solution”, “distributional solutions”, “level set”
-
Elementary discrete diffusion/redistancing schemes for the mean curvature flow
Topics Mean curvature flow · Same authors Antonin Chambolle, Daniele De Gennaro, Massimiliano Morini
-
Discrete-to-continuum crystalline curvature flows
Topics Mean curvature flow · Same authors Antonin Chambolle, Daniele De Gennaro, Massimiliano Morini
Read around it
Background reading
The guides for the topics of this paper: what each idea is, why it matters, and the papers to read first.
In the guidebook
- 11A.13Homogeneous Flows
A computable laboratory: the flow on Thurston’s geometries.
- 12C.9After Perelman
Singular flows, the Smale conjecture, and Bamler’s theory.
- 6A.10Curve Shortening and the First Geometric Flows
Shrinking circles, grim reapers, neckpinches and Huisken’s monotonicity, seen in the plane.