Fractional mean curvature flow of Lipschitz graphs
نویسندگان
چکیده
Abstract We consider the fractional mean curvature flow of entire Lipschitz graphs. provide regularity results, and we study long time asymptotics flow. In particular show that in a suitable rescaled framework, if initial graph is sublinear perturbation cone, evolution asymptotically approaches an expanding self-similar solution. also prove stability hyperplanes convex cones unrescaled setting.
منابع مشابه
Lagrangian mean curvature flow for entire Lipschitz graphs II
We prove longtime existence and estimates for smooth solutions to a fully nonlinear Lagrangian parabolic equation with locally C1,1 initial data u0 satisfying either (1) −(1+ η)In ≤ Du0 ≤ (1+ η)In for some positive dimensional constant η, (2) u0 is weakly convex everywhere, or (3) u0 verifies a large supercritical Lagrangian phase condition. Mathematics Subject Classification (2000) Primary 53C...
متن کاملLagrangian Mean Curvature Flow for Entire Lipschitz Graphs
We consider the mean curvature flow of entire Lagrangian graphs with Lipschitz continuous initial data. Assuming only a certain bound on the Lipschitz norm of an initial entire Lagrangian graph in R, we show that the parabolic equation (1.1) has a longtime solution which is smooth for all positive time and satisfies uniform estimates away from time t = 0. In particular, under the mean curvature...
متن کاملThe Mean Curvature Flow Smoothes Lipschitz Submanifolds
The mean curvature flow is the gradient flow of volume functionals on the space of submanifolds. We prove a fundamental regularity result of mean curvature flow in this paper: a Lipschitz submanifold with small local Lipschitz norm becomes smooth instantly along the mean curvature flow. This generalizes the regularity theorem of Ecker and Huisken for Lipschitz hypersurfaces. In particular, any ...
متن کاملMean curvature flow of spacelike graphs
We prove the mean curvature flow of a spacelike graph in (Σ1 ×Σ2,g1 −g2) of a map f : Σ1 → Σ2 from a closed Riemannian manifold (Σ1,g1) with Ricci1 > 0 to a complete Riemannian manifold (Σ2,g2) with bounded curvature tensor and derivatives, and with K2 ≤ K1, remains a spacelike graph, exists for all time, and converges to a slice at infinity. We also show, with no need of the assumption K2 ≤ K1...
متن کاملMean Curvature Blowup in Mean Curvature Flow
In this note we establish that finite-time singularities of the mean curvature flow of compact Riemannian submanifolds M t →֒ (N, h) are characterised by the blow up of the mean curvature.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Manuscripta Mathematica
سال: 2022
ISSN: ['0025-2611', '1432-1785']
DOI: https://doi.org/10.1007/s00229-022-01371-5