Approximation by Lipschitz functions

TL;DR

This paper characterizes functions on metric spaces that can be uniformly approximated by Lipschitz functions, with applications to complex analysis on Riemannian manifolds and symmetric domains.

Contribution

It provides an intrinsic characterization of functions approximable by Lipschitz functions on metric spaces, extending to complex analysis contexts.

Findings

Characterization of functions as uniform limits of Lipschitz functions

Applications to function theory on Riemannian manifolds

Applications to bounded symmetric domains

Abstract

On any metric space, I provide an intrinsic characterization of those complex-valued functions which are uniform limits of Lipschitz functions. There are applications to function theory on complete Riemannian manifolds and, in particular, on bounded symmetric domains in complex Euclidean space.