2-Dimensional flat curvature flow of crystals

  • David G. Caraballo

    Georgetown University, Washington, USA


In the impressive and seminal paper \cite{ATW}, Fred Almgren, Jean Taylor, and Lihe Wang introduced flat curvature flow in , a variational time-discretization scheme for (isotropic or anisotropic) mean curvature flow. Their main result asserts the H\"{o}lder continuity, in time, of these flows. This essential estimate requires a boundary regularity result, a uniform lower density ratio bound condition, which they proved for each Similar estimates for Brownian flows, from important work by N.K Yip on stochastic mean curvature flow \cite{Yip}, also rely on this pivotal regularity result. In this paper, we complete these analyses for the case by establishing the necessary uniform lower density ratio bounds. MSC 2000 subject classification: 53C44, 49Q20, 49N60.

Cite this article

David G. Caraballo, 2-Dimensional flat curvature flow of crystals. Interfaces Free Bound. 7 (2005), no. 3, pp. 241–254

DOI 10.4171/IFB/123