# Differential inequalities of continuous functions and removing singularities of Rado type for J-holomorphic maps - Mathematics > Complex Variables

Differential inequalities of continuous functions and removing singularities of Rado type for J-holomorphic maps - Mathematics > Complex Variables - Download this document for free, or read online. Document in PDF available to download.

Abstract: We consider a continuous function $f$ on a domain in $\mathbf C^n$ satisfyingthe inequality that $|\bar \partial f|\leq |f|$ off its zero set. The mainconclusion is that the zero set of $f$ is a complex variety.We also obtain removable singularity theorem of Rado type for J-holomorphicmaps. Let $\Omega$ be an open subset in $\mathbf C$ and let $E$ be a closedpolar subset of $\Omega$. Let $u$ be a continuous map from $\Omega$ into analmost complex manifold $M,J$ with $J$ of class $C^1$. We show that if $u$ isJ-holomorphic on $\Omega\setminus E$ then it is J-holomorphic on $\Omega$.

Author: ** Xianghong Gong, Jean-Pierre Rosay**

Source: https://arxiv.org/