Plurisubharmonic functions and real submanifolds of $\C^n$

TL;DR

This paper provides estimates for the volume of analytic varieties near real submanifolds in complex space, with applications to measure theory and integrability of plurisubharmonic functions.

Contribution

It introduces new volume estimates for analytic varieties near real submanifolds and explores their implications for measure and integrability properties.

Findings

Volume estimates for analytic varieties near real submanifolds

Bounds on Hausdorff measure of intersections

Exponential integrability results for plurisubharmonic functions

Abstract

We give an estimate for the volume of an analytic variety (or more generally the mass of a positive closed current) close to a real submanifold $M$. Applications are given to the Hausdorff measure of the intersection of the variety with $M$ and the exponential integrability of plurisubharmonic functions on $M$.