2-Dimensional flat curvature flow of crystals

  • David G. Caraballo

    Georgetown University, Washington, USA


In the impressive and seminal paper [5], 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 Hölder 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 [30], 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.

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