We provide a direct proof of a non-collapsing estimate for compact hypersurfaces with positive mean curvature moving under the mean curvature flow: Precisely, if every point on the initial hypersurface admits an interior sphere with radius inversely proportional to the mean curvature at that point, then this remains true for all positive times in the interval of existence. We follow [4] in defi...

In this note we announce results on the mean curvature flow of mean convex sets in 3-dimensions. Loosely speaking, our results justify the naive picture of mean curvature flow where the only singularities are neck pinches, and components which collapse to asymptotically round spheres. In this note we announce results on the mean curvature flow of mean convex sets; all the statements below have ...

gas motion within the cylinder is one of the major factors that control the combustion process in spark ignition engine. it also has significant impact on heat transfer. both the bulk gas motion and the turbulence characteristics of the flow are important and governing the overall behavior of the flow. an arrangement for obtaining a stratified charge, using port injection, is proposed for a cur...