# On the Maximal Gaussian Perimeter of Convex Sets, Revisited

## TL;DR

This paper revisits Nazarov's construction of convex sets with nearly maximal Gaussian surface area, offering an alternative analysis using convex influence to deepen understanding of Gaussian perimeter extremal problems.

## Contribution

It provides a new analysis framework for Nazarov's construction, enhancing the understanding of Gaussian surface area maximization for convex sets.

## Key findings

- Nazarov's convex set nearly maximizes Gaussian surface area.
- An alternative analysis based on convex influence is proposed.
- The approach offers new insights into Gaussian perimeter extremal problems.

## Abstract

We revisit Nazarov's construction of a convex set with nearly maximal Gaussian surface area and give an alternate analysis based on the notion of convex influence.