scholarly journals Extension of Two-Dimensional Mean Curvature Flow with Free Boundary

2019 ◽  
Author(s):  
Siao-Hao Guo
Keyword(s):  
Free Boundary ◽  
Mean Curvature ◽  
Mean Curvature Flow ◽  
Curvature Flow ◽  
Two Dimensional

scholarly journals Mean curvature flow with free boundary outside a hypersphere

2017 ◽  
Vol 369 (12) ◽  
pp. 8319-8342 ◽  
Author(s):  
Glen Wheeler ◽  
Valentina-Mira Wheeler
Keyword(s):  
Free Boundary ◽  
Mean Curvature ◽  
Mean Curvature Flow ◽  
Curvature Flow

scholarly journals The free-boundary Brakke flow

2020 ◽  
Vol 2020 (758) ◽  
pp. 95-137 ◽  
Author(s):  
Nick Edelen
Keyword(s):  
Free Boundary ◽  
Mean Curvature ◽  
Mean Curvature Flow ◽  
Curvature Flow ◽  
Monotonicity Formula ◽  
Local Regularity ◽  
Regularity Theorem ◽  
Elliptic Regularization ◽  
Barrier Surface ◽  
Boundary Mean Curvature

AbstractWe develop the notion of Brakke flow with free-boundary in a barrier surface. Unlike the classical free-boundary mean curvature flow, the free-boundary Brakke flow must “pop” upon tangential contact with the barrier. We prove a compactness theorem for free-boundary Brakke flows, define a Gaussian monotonicity formula valid at all points, and use this to adapt the local regularity theorem of White [23] to the free-boundary setting. Using Ilmanen’s elliptic regularization procedure [10], we prove existence of free-boundary Brakke flows.

Skew mean curvature flow

2019 ◽  
Vol 21 (01) ◽  
pp. 1750090
Author(s):  
Chong Song ◽  
Jun Sun
Keyword(s):  
Mean Curvature ◽  
Mean Curvature Flow ◽  
Curvature Flow ◽  
Embedding Theorem ◽  
Sobolev Type ◽  
Two Dimensional ◽  
Initial Value ◽  
Codimension Two ◽  
Surfaces In Euclidean Space ◽  
Short Time

The skew mean curvature flow (SMCF), which origins from the study of fluid dynamics, describes the evolution of a codimension two submanifold along its binormal direction. We study the basic properties of the SMCF and prove the existence of a short-time solution to the initial value problem of the SMCF of compact surfaces in Euclidean space [Formula: see text]. A Sobolev-type embedding theorem for the second fundamental forms of two-dimensional surfaces is also proved, which might be of independent interest.

scholarly journals Mean curvature flow with free boundary – Type 2 singularities

2020 ◽  
Vol 293 (4) ◽  
pp. 794-813
Author(s):  
Glen Wheeler ◽  
Valentina‐Mira Wheeler
Keyword(s):  
Free Boundary ◽  
Mean Curvature ◽  
Mean Curvature Flow ◽  
Curvature Flow ◽  
Boundary Type

Two-Dimensional Graphs Moving by Mean Curvature Flow

2002 ◽  
Vol 18 (2) ◽  
pp. 209-224 ◽  
Author(s):  
Jing Yi Chen ◽  
Jia Yu Li ◽  
Gang Tian
Keyword(s):  
Mean Curvature ◽  
Mean Curvature Flow ◽  
Curvature Flow ◽  
Two Dimensional
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