Hölder regularity of generic manifold

Abstract

In this paper we study Hölder continuity of the pluricomplex Green function with logarithmic growth at infinity of a smooth generic submanifold of $\C^n$. In particular we prove that the pluricomplex Green function of any $C^2$-smooth generic compact submanifold of $\C^n$ (without boundary) is Lipschitz continuous in $\C^n$.

To appear in Ann. Scuola Norm. Sup. Pisa Cl. Sci. in 2016; 14 pages