H\"older regularity of generic manifold

TL;DR

This paper proves that the pluricomplex Green function associated with any smooth, boundaryless, generic submanifold in complex n-space is Lipschitz continuous, establishing a regularity result in pluripotential theory.

Contribution

It demonstrates the Lipschitz continuity of the pluricomplex Green function for smooth generic submanifolds, extending regularity results in complex analysis.

Findings

Pluricomplex Green function is Lipschitz continuous for smooth generic submanifolds.

The result applies to submanifolds without boundary.

The study advances understanding of regularity in pluripotential theory.

Abstract

In this paper we study H\"older 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 $\C^n$.