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

DOI: http://dx.doi.org/10.4310/CAG.2008.v16.n4.a4

Author

Giuseppe Tinaglia (University of Notre Dame, Indiana)

Abstract

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.

Full Text (PDF format)