Communications in Analysis and Geometry

Volume 16 (2008)

Number 4

Structure theorems for embedded disks with mean curvature bounded in $L^p$

Pages: 819 – 836



Giuseppe Tinaglia (University of Notre Dame, Indiana)


After appropriate normalizations, an embedded disk with secondfundamental form large at a point contains a multi-valued grapharound that point, provided the $L^p$ norm of the mean curvature issufficiently small. This generalizes to non-minimal surfaces awell-known result of Colding and Minicozzi.

Published 1 January 2008