Doubling property for biLipschitz homogeneous geodesic surfaces

TL;DR

This paper investigates geodesic surfaces with local biLipschitz homogeneity, proving they are locally doubling and establishing a special doubling measure similar to Haar measure.

Contribution

It introduces the property that such surfaces are locally doubling and constructs a corresponding special doubling measure.

Findings

Geodesic surfaces with local biLipschitz homogeneity are locally doubling.

Existence of a special doubling measure analogous to Haar measure.

Provides foundational properties for these surfaces.

Abstract

In this paper we discuss general properties of geodesic surfaces that are locally biLipschitz homogeneous. In particular, we prove that they are locally doubling and that there exists a special doubling measure analogous to the Haar measure for locally compact groups.