Singular Perturbations of Mean Curvature Flow
نویسندگان
چکیده
We introduce a regularization method for mean curvature flow of a submanifold of arbitrary codimension in the Euclidean space, through higher order equations. We prove that the regularized problems converge to the mean curvature flow for all times before the first singularity.
منابع مشابه
Singularities of Symplectic and Lagrangian Mean Curvature Flows
In this paper we study the singularities of the mean curvature flow from a symplectic surface or from a Lagrangian surface in a Kähler-Einstein surface. We prove that the blow-up flow Σ∞ s at a singular point (X0, T0) of a symplectic mean curvature flow Σt or of a Lagrangian mean curvature flow Σt is a non trivial minimal surface in R, if Σ∞ −∞ is connected.
متن کاملA Note on Singular Time of Mean Curvature Flow
We show that mean curvature flow of a compact submanifold in a complete Riemannian manifold cannot form singularity at time infinity if the ambient Riemannian manifold has bounded geometry and satisfies certain curvature and volume growth conditions .
متن کاملConvergence of Perturbed Allen–cahn Equations to Forced Mean Curvature Flow
We study perturbations of the Allen–Cahn equation and prove the convergence to forced mean curvature flow in the sharp interface limit. We allow for perturbations that are square-integrable with respect to the diffuse surface area measure. We give a suitable generalized formulation for forced mean curvature flow and apply previous results for the Allen–Cahn action functional. Finally we discuss...
متن کاملUniversality in Mean Curvature Flow Neckpinches
We study noncompact surfaces evolving by mean curvature flow. Without any symmetry assumptions, we prove that any solution that is C3close at some time to a standard neck will develop a neckpinch singularity in finite time, will become asymptotically rotationally symmetric in a space-time neighborhood of its singular set, and will have a unique tangent flow.
متن کاملNonconvex mean curvature flow as a formal singular limit of the nonlinear bidomain model
In this paper we study the nonconvex anisotropic mean curvature flow of a hypersurface. This corresponds to an anisotropic mean curvature flow where the anisotropy has a nonconvex Frank diagram. The geometric evolution law is therefore forward-backward parabolic in character, hence ill-posed in general. We study a particular regularization of this geometric evolution, obtained with a nonlinear ...
متن کامل