Anisotropic and crystalline mean curvature flow

Matteo Novaga (Università di Pisa)

I will present existence and uniqueness results for the anisotropic 
mean curvature flow with arbitrary mobility. Th is achieved by 
introducing a new notion of solution to the corresponding level 
set formulation. Such a solution satisfies the comparison principle 
and a stability property with respect to the approximation by 
suitably regularized problems. The results are valid in any 
dimension and for arbitrary, possibly unbounded, initial 
closed sets.

The approach accounts for the possible presence of a time-dependent 
bounded forcing term, with spatial Lipschitz continuity. 
As a byproduct of the analysis, the problem of the convergence 
of the Almgren-Taylor-Wang minimizing movements scheme to a 
unique "flat flow" in the case of general, possibly crystalline, 
anisotropies is settled.