Improved $C^{1,1}$ regularity for multiple membranes problem

Abstract

We prove the $C^{1,1}$-regularity for stationary $C^{1,\hat{I}\pm }$ ($\hat{I}\pm \in (0,1)$) solutions to the multiple membrane problem. This regularity estimate was essentially used in our recent work on Yau's four minimal spheres conjecture.

44 pages; minor revisions; comments welcome