The weak min-max property in Banach spaces

TL;DR

This paper explores the weak min-max property in Banach spaces, linking it to diameter uniformity of domains and demonstrating invariance under certain mappings, advancing understanding of geometric properties in functional analysis.

Contribution

It establishes a connection between the weak min-max property and diameter uniformity, and shows invariance of diameter uniform domains under relatively quasim"obius mappings.

Findings

Diameter uniform domains are invariant under relatively quasim"obius mappings.

The weak min-max property relates to the diameter uniformity in Banach spaces.

The study extends geometric analysis in Banach space theory.

Abstract

In this paper, we investigate the relationship between the weak min-max property and the diameter uniformity of domains in Banach spaces with dimensions at least $2$. As an application, we show that diameter uniform domains are invariant under relatively quasim\"obius mappings.