scholarly journals Convexity estimates for mean curvature flow with free boundary

2016 ◽  
Vol 294 ◽  
pp. 1-36 ◽  
Author(s):  
Nick Edelen
Keyword(s):  
Free Boundary ◽  
Mean Curvature ◽  
Mean Curvature Flow ◽  
Curvature Flow

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 Mean Convex Mean Curvature Flow with Free Boundary

2021 ◽  
Author(s):  
Nick Edelen ◽  
Robert Haslhofer ◽  
Mohammad N. Ivaki ◽  
Jonathan J. Zhu
Keyword(s):  
Free Boundary ◽  
Mean Curvature ◽  
Mean Curvature Flow ◽  
Curvature Flow ◽  
Mean Convex

scholarly journals Evolution of the first eigenvalue of the Laplace operator and the p-Laplace operator under a forced mean curvature flow

2020 ◽  
Vol 18 (1) ◽  
pp. 1518-1530
Author(s):  
Xuesen Qi ◽  
Ximin Liu
Keyword(s):  
Laplace Operator ◽  
Mean Curvature ◽  
Mean Curvature Flow ◽  
Curvature Flow ◽  
Second Fundamental Form ◽  
Coefficient Function ◽  
First Eigenvalue ◽  
Initial Hypersurface ◽  
The Mean ◽  
The Laplace Operator

Abstract In this paper, we discuss the monotonicity of the first nonzero eigenvalue of the Laplace operator and the p-Laplace operator under a forced mean curvature flow (MCF). By imposing conditions associated with the mean curvature of the initial hypersurface and the coefficient function of the forcing term of a forced MCF, and some special pinching conditions on the second fundamental form of the initial hypersurface, we prove that the first nonzero closed eigenvalues of the Laplace operator and the p-Laplace operator are monotonic under the forced MCF, respectively, which partially generalize Mao and Zhao’s work. Moreover, we give an example to specify applications of conclusions obtained above.

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