Long-time existence and convergence of graphic mean curvature flow in arbitrary codimension
نویسندگان
چکیده
منابع مشابه
Long-time Existence and Convergence of Graphic Mean Curvature Flow in Arbitrary Codimension
Let f : Σ1 7→ Σ2 be a map between compact Riemannian manifolds of constant curvature. This article considers the evolution of the graph of f in Σ1×Σ2 by the mean curvature flow. Under suitable conditions on the curvature of Σ1 and Σ2 and the differential of the initial map, we show that the flow exists smoothly for all time. At each instant t, the flow remains the graph of a map ft and ft conve...
متن کاملLevel set approach to mean curvature flow in arbitrary codimension
We develop a level set theory for the mean curvature evolution of surfaces with arbitrary co-dimension, thus generalizing the previous work [6, 13] on hypersurfaces. The main idea is to surround the evolving surface of co-dimension k in R by a family of hypersurfaces (the level sets of a function) evolving with normal velocity equal to the sum of the (d − k) smallest principal curvatures. The e...
متن کاملMean Curvature Flow of Higher Codimension in Hyperbolic Spaces
where H(x, t) is the mean curvature vector of Ft(M) and Ft(x) = F (x, t). We call F : M × [0, T ) → F(c) the mean curvature flow with initial value F . The mean curvature flow was proposed by Mullins [17] to describe the formation of grain boundaries in annealing metals. In [3], Brakke introduced the motion of a submanifold by its mean curvature in arbitrary codimension and constructed a genera...
متن کاملLong time behavior of Riemannian mean curvature flow of graphs
In this paper we consider long time behavior of a mean curvature flow of nonparametric surface in Rn, with respect to a conformal Riemannian metric. We impose zero boundary value, and we prove that the solution tends to 0 exponentially fast as t → ∞. Its normalization u/supu tends to the first eigenfunction of the associated linearized problem. 2002 Elsevier Science (USA). All rights reserved.
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: Inventiones mathematicae
سال: 2002
ISSN: 0020-9910,1432-1297
DOI: 10.1007/s002220100201