an:00205133
Zbl 0783.35002
Almgren, Fred; Taylor, Jean E.; Wang, Lihe
Curvature-driven flows: a variational approach
EN
SIAM J. Control Optimization 31, No. 2, 387-438 (1993).
00013173
1993
j
35A15 35K99 49Q20 58E99
solids with non-smooth surfaces; curvature evolution; flat curvature flow; motion-by-mean curvature; weighted mean curvature; currents; calculus of variations; geometric measure theory; mean curvature; curvature flows for solids
The authors study curvature flows for solids. When the solids have smooth surfaces, this flow can be described as that generated by the vector field which, at each point on the surface, equals the mean curvature vector of the surface at that point. The interest here is in solids which do not have smooth surfaces, such as polyhedra. In addition, the flow needs not to be generated by the (appropriate generalization of the) mean curvature; in general the mean curvature, which comes from the variational function \(f(p)=| p |\) (where \(p\) denotes the normal to the surface), is replaced by a curvature generated from a function \(f\) which is continuous, even, positively homogeneous of degree 1, and smooth on \(\mathbb{R}^{n+1}\backslash\{0\}\).
G.M.Lieberman (Ames)