Uniqueness of Self-similar Shrinkers with Asymptotically Conical Ends
نویسنده
چکیده
Here H = div (n) is the mean curvature, n is the outward unit normal, x is the position vector and 〈, 〉 denotes the Euclidean inner product. One reason that selfshrinking solutions to the mean curvature flow are particularly interesting is that they provide singularity models of the flow; see [20, 21], [24] and [46]. Throughout, O is the origin of R; BR denotes the open ball in R n+1 centered at O with radius R and SR = ∂BR; DR denotes the open disk in R n×{0} centered at the origin with radius R. We say that C ⊂ R is a regular cone with vertex at O, if
منابع مشابه
Uniqueness of Self-similar Shrinkers with Asymptotically Cylindrical Ends
In this paper, we show the uniqueness of smooth embedded selfshrinkers asymptotic to generalized cylinders of infinite order. Also, we construct non-rotationally symmetric self-shrinking ends asymptotic to generalized cylinders with rate as fast as any given polynomial.
متن کاملA Bernstein Type Theorem for Self-similar Shrinkers
In this note, we prove that smooth self-shrinkers in R, that are entire graphs, are hyperplanes. Previously Ecker and Huisken showed that smooth self-shrinkers, that are entire graphs and have at most polynomial growth, are hyperplanes. The point of this note is that no growth assumption at infinity is needed.
متن کاملar X iv : 1 60 9 . 02 10 5 v 1 [ m at h . D G ] 7 S ep 2 01 6 ROTATIONAL SYMMETRY OF ASYMPTOTICALLY CONICAL MEAN CURVATURE FLOW SELF - EXPANDERS
In this article, we examine complete, mean-convex self-expanders for the mean curvature flow whose ends have decaying principal curvatures. We prove a Liouville-type theorem associated to this class of self-expanders. As an application, we show that mean-convex self-expanders which are asymptotic to O(n)-invariant cones are rotationally symmetric.
متن کاملSmooth Compactness of Self-shrinkers
We prove a smooth compactness theorem for the space of embedded selfshrinkers in R. Since self-shrinkers model singularities in mean curvature flow, this theorem can be thought of as a compactness result for the space of all singularities and it plays an important role in studying generic mean curvature flow. 0. Introduction A surface Σ ⊂ R is said to be a self-shrinker if it satisfies (0.1) H ...
متن کاملTransverse Sensing of Simply Supported Truncated Conical Shells
Modal signals of transverse sensing of truncated conical shells with simply supported boundary condition at both ends are investigated. The embedded piezoelectric layer on the surface of conical shell is used as sensors and output voltages of them in considered modes are calculated. The Governing sensing signal displacement equations are derived based on the Kirchhoff theory, thin-shell assumpt...
متن کامل