Mean curvature flow and self-similar submanifolds
نویسندگان
چکیده
منابع مشابه
The 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 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 کاملEntire Self-similar Solutions to Lagrangian Mean Curvature Flow
Abstract. We consider self-similar solutions to mean curvature evolution of entire Lagrangian graphs. When the Hessian of the potential function u has eigenvalues strictly uniformly between −1 and 1, we show that on the potential level all the shrinking solitons are quadratic polynomials while the expanding solitons are in one-to-one correspondence to functions of homogenous of degree 2 with th...
متن کاملMean Curvature Flow of Pinched Submanifolds to Spheres
The evolution of hypersurfaces by their mean curvature has been studied by many authors since the appearance of Gerhard Huisken’s seminal paper [Hu1]. More recently, mean curvature flow of higher codimension submanifolds has also received attention. In this paper we prove a result analogous to that of [Hu1] for submanifolds of any codimension. Let F0 : Σn → Rn+k be a smooth immersion of a compa...
متن کاملSingularity of Mean Curvature Flow of Lagrangian Submanifolds
In this article we study the tangent cones at first time singularity of a Lagrangian mean curvature flow. If the initial compact submanifold Σ0 is Lagrangian and almost calibrated by ReΩ in a Calabi-Yau n-fold (M,Ω), and T > 0 is the first blow-up time of the mean curvature flow, then the tangent cone of the mean curvature flow at a singular point (X0, T ) is a stationary Lagrangian integer mul...
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: Séminaire de théorie spectrale et géométrie
سال: 2003
ISSN: 2118-9242
DOI: 10.5802/tsg.332