Why bootstrapping for $J$-holomorphic curves fails in $C^k$

Hansjörg Geiges, Murat Sağlam, Kai Zehmisch

We present a simple example for the failure of the Calderón-Zygmund estimate for the $\bar{\partial }$-operator when the Sobolev $(k,p)$-norms are replaced by the $C^k$-norms. This…