scholarly journals Mean curvature flow of entire graphs in a half-space with a free boundary

2014 ◽  
Vol 2014 (690) ◽  
Author(s):  
Valentina Mira Wheeler
Keyword(s):  
Free Boundary ◽  
Half Space ◽  
Mean Curvature ◽  
Mean Curvature Flow ◽  
Curvature Flow ◽  
Entire Graphs

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.

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

scholarly journals Evolution of convex entire graphs by curvature flows

2015 ◽  
Vol 1 (1) ◽  
Author(s):  
Roberta Alessandroni ◽  
Carlo Sinestrari
Keyword(s):  
Euclidean Space ◽  
Initial Data ◽  
Mean Curvature ◽  
Symmetric Function ◽  
Mean Curvature Flow ◽  
Curvature Flow ◽  
Principal Curvatures ◽  
The Mean ◽  
Entire Graphs

AbstractWe consider the evolution of an entire convex graph in euclidean space with speed given by a symmetric function of the principal curvatures. Under suitable assumptions on the speed and on the initial data, we prove that the solution exists for all times and it remains a graph. In addition, after appropriate rescaling, it converges to a homothetically expanding solution of the flow. In this way, we extend to a class of nonlinear speeds the well known results of Ecker and Huisken for the mean curvature flow.

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