scholarly journals Existence and uniqueness for planar anisotropic and crystalline curvature flow

2019 ◽  
Author(s):  
Antonin Chambolle ◽  
Matteo Novaga
Keyword(s):  
Existence And Uniqueness ◽  
Curvature Flow ◽  
Crystalline Curvature

scholarly journals Two examples of nonconvex self-similar solution curves for a crystalline curvature flow

2004 ◽  
Vol 80 (8) ◽  
pp. 151-154 ◽  
Author(s):  
Tetsuya Ishiwata ◽  
Takeo K. Ushijima ◽  
Hiroki Yagisita ◽  
Shigetoshi Yazaki
Keyword(s):  
Curvature Flow ◽  
Similar Solution ◽  
Self Similar Solution ◽  
Self Similar ◽  
Crystalline Curvature

scholarly journals Weak solutions of inverse mean curvature flow for hypersurfaces with boundary

2017 ◽  
Vol 2017 (728) ◽  
Author(s):  
Thomas Marquardt
Keyword(s):  
Boundary Condition ◽  
Weak Solutions ◽  
Mean Curvature ◽  
Existence And Uniqueness ◽  
Mean Curvature Flow ◽  
Curvature Flow ◽  
Inverse Mean Curvature Flow ◽  
Closed Hypersurfaces ◽  
Neumann Type

AbstractWe consider the evolution of hypersurfaces with boundary under inverse mean curvature flow. The boundary condition is of Neumann type, i.e. the evolving hypersurface moves along, but stays perpendicular to, a fixed supporting hypersurface. In this setup, we prove existence and uniqueness of weak solutions. Furthermore, we indicate the existence of a monotone quantity which is the analog of the Hawking mass for closed hypersurfaces.

scholarly journals Existence and Uniqueness for a Crystalline Mean Curvature Flow

2016 ◽  
Vol 70 (6) ◽  
pp. 1084-1114 ◽  
Author(s):  
Antonin Chambolle ◽  
Massimiliano Morini ◽  
Marcello Ponsiglione
Keyword(s):  
Mean Curvature ◽  
Existence And Uniqueness ◽  
Mean Curvature Flow ◽  
Curvature Flow

NONUNIQUENESS FOR CRYSTALLINE CURVATURE FLOW

2007 ◽  
Vol 17 (08) ◽  
pp. 1307-1315
Author(s):  
MATTEO NOVAGA ◽  
MAURIZIO PAOLINI
Keyword(s):  
Curvature Flow ◽  
Wulff Shape ◽  
Crystalline Curvature

We discuss some examples of nonuniqueness for the crystalline curvature flow, when the Wulff shape is a square not centered at the origin.

scholarly journals Local existence and uniqueness of skew mean curvature flow

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Chong Song
Keyword(s):  
Fluid Dynamics ◽  
Mean Curvature ◽  
Existence And Uniqueness ◽  
Mean Curvature Flow ◽  
Local Existence ◽  
Curvature Flow ◽  
Vortex Filament ◽  
Euclidean Spaces ◽  
Geometric Flow ◽  
Local Existence And Uniqueness

Abstract The Skew Mean Curvature Flow (SMCF) is a Schrödinger-type geometric flow canonically defined on a co-dimension two submanifold, which generalizes the famous vortex filament equation in fluid dynamics. In this paper, we prove the local existence and uniqueness of general-dimensional SMCF in Euclidean spaces.

scholarly journals Crystalline curvature flow of planar networks

2006 ◽  
pp. 481-521 ◽  
Author(s):  
Giovanni Bellettini ◽  
M. Chermisi ◽  
Matteo Novaga
Keyword(s):  
Curvature Flow ◽  
Crystalline Curvature ◽  
Planar Networks
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