Compactness Results for Sequences of Approximate Biharmonic Maps

In this article, we prove energy quantization for approximate (intrinsic and extrinsic) biharmonic maps into spheres where the approximate map is in $L \log L$. Moreover, we demonstrate that if the $L\log L$ norm of the approximate maps does not concentrate, the image of the bubbles are connected without necks

Helicoid-Like Minimal Disks and Uniqueness

We show that an embedded minimal disk in R^3 with large curvature is bilipschitz with a piece of a helicoid. Additionally, a simplified proof of the uniqueness of the helicoid is provided.Comment: 17 pages, LaTex; substantially expanded and revised per referee's suggestions; To appear J. Reine. Angew. Mat