Jacob Reznikov (Massachusetts Institute of Technology)
Geometric Analysis Seminar
Title:聽Inscribed Curvature Bounds for Graphical Hypersurfaces.
础产蝉迟谤补肠迟:听The inscribed curvature of a hypersurface, introduced by Andrews in the study of non-collapsing for mean curvature flow, measures the inverse radius of the largest ball that fits inside the surface at a given point. While the second fundamental form immediately controls the inscribed curvature from below, the reverse inequality fails for general hypersurfaces. We derive an interior inscribed curvature estimate for graphical hypersurfaces in Riemannian cylinders NxR, depending only on the second fundamental form of the surface and the ambient curvature. The proof uses a novel chord-arc bound for graphical surfaces at the scale of their curvature. As applications we obtain a Heinz-type inscribed curvature estimate for minimal graphs and uniform area bounds for graphical hypersurfaces in curved ambient spaces.