scholarly journals Uniqueness and existence of viscosity solutions of generalized mean curvature flow equations

1991 ◽  
Vol 33 (3) ◽  
pp. 749-786 ◽  
Author(s):  
Yun Gang Chen ◽  
Yoshikazu Giga ◽  
Shun'ichi Goto
Keyword(s):  
Viscosity Solutions ◽  
Mean Curvature ◽  
Mean Curvature Flow ◽  
Curvature Flow ◽  
Flow Equations ◽  
Generalized Mean Curvature ◽  
Generalized Mean ◽  
Uniqueness And Existence

scholarly journals On the horizontal mean curvature flow for axisymmetric surfaces in the Heisenberg group

2014 ◽  
Vol 16 (03) ◽  
pp. 1350027 ◽  
Author(s):  
Fausto Ferrari ◽  
Qing Liu ◽  
Juan J. Manfredi
Keyword(s):  
Heisenberg Group ◽  
Level Set Method ◽  
Level Set ◽  
Viscosity Solutions ◽  
Mean Curvature ◽  
Explicit Solution ◽  
Mean Curvature Flow ◽  
Curvature Flow ◽  
Existence And Stability ◽  
The Mean

We study the horizontal mean curvature flow in the Heisenberg group by using the level-set method. We prove the uniqueness, existence and stability of axisymmetric viscosity solutions of the level-set equation. An explicit solution is given for the motion starting from a subelliptic sphere. We also give several properties of the level-set method and the mean curvature flow in the Heisenberg group.

A Class of Parabolic Equations Driven by the Mean Curvature Flow

2018 ◽  
Vol 62 (1) ◽  
pp. 135-163
Author(s):  
Anderson L. A. de Araujo ◽  
Marcelo Montenegro
Keyword(s):  
Parabolic Equations ◽  
Mean Curvature ◽  
Approximation Scheme ◽  
Mean Curvature Flow ◽  
Curvature Flow ◽  
Dirichlet Condition ◽  
Parabolic Problems ◽  
Cylindrically Symmetric ◽  
Generalized Mean Curvature ◽  
The Mean

AbstractWe study a class of parabolic equations which can be viewed as a generalized mean curvature flow acting on cylindrically symmetric surfaces with a Dirichlet condition on the boundary. We prove the existence of a unique solution by means of an approximation scheme. We also develop the theory of asymptotic stability for solutions of general parabolic problems.

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