We establish regularity results for critical points to energies of immersed surfaces depending on the first and the second fundamental form exclusively. These results hold for a large class of intrinsic elliptic Lagrangians which are sub-critical or critical. They are derived using uniform ϵ-regularity estimates which do not degenerate as the Lagrangians approach the critical regime given by the Willmore integrand.
|Number of pages||39|
|Journal||Calculus of Variations and Partial Differential Equations|
|Publication status||Published - 1 Feb 2019|