Asymptotics for optimal controls for horizontal mean curvature flow
نویسندگان
چکیده
منابع مشابه
Mean 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 کاملLocal Techniques for Mean Curvature Flow
of ann-dimensional manifold without boundary into Euclidean space. We say Af = x(Mn) moves by mean curvature if there exists a one-parameter family Xt = x( ·, t) of immersions with corresponding images J..!I1 = x 1(lvfn) satisfying d dtx(p,t) = -H(p,t)v(p,t) (1) x(p,O) = xo(P) for some initial data xo. Here H(p,t) and v(p,t) denote mean curvature and outer unit normal of the hypersurface M 1 at...
متن کاملThe Mean Curvature Flow for Isoparametric Submanifolds
A submanifold in space forms is isoparametric if the normal bundle is flat and principal curvatures along any parallel normal fields are constant. We study the mean curvature flow with initial data an isoparametric submanifold in Euclidean space and sphere. We show that the mean curvature flow preserves the isoparametric condition, develops singularities in finite time, and converges in finite ...
متن کاملMean curvature flow
Mean curvature flow is the negative gradient flow of volume, so any hypersurface flows through hypersurfaces in the direction of steepest descent for volume and eventually becomes extinct in finite time. Before it becomes extinct, topological changes can occur as it goes through singularities. If the hypersurface is in general or generic position, then we explain what singularities can occur un...
متن کاملRiemannian Mean Curvature Flow
In this paper we explicitly derive a level set formulation for mean curvature flow in a Riemannian metric space. This extends the traditional geodesic active contour framework which is based on conformal flows. Curve evolution for image segmentation can be posed as a Riemannian evolution process where the induced metric is related to the local structure tensor. Examples on both synthetic and re...
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: Nonlinear Analysis
سال: 2021
ISSN: 0362-546X
DOI: 10.1016/j.na.2020.112076