Geometric analysis of metric spaces is a vibrant research area at the interface of analysis, geometry and topology. It examines the intrinsic structure of spaces endowed with a notion of distance, ...

Banach spaces provide a fundamental framework for analysing problems in functional analysis, encapsulating the notion of complete normed vector spaces. Metric geometry, by contrast, concerns itself ...

In this article, we introduce a McShane type integral on a complete metric space, endowed with a Radon measure μ with a family of cells that satisfies the Vitali covering theorem with respect to μ.

In this paper, we study the asymptotic behavior of the volume of spheres in metric measure spaces. We first introduce a general setting adapted to the study of asymptotic isoperimetry in a general ...