Equivariant Smoothing Processes on Currents and Spaces with Bounded Curvature

TL;DR

This paper develops equivariant smoothing techniques for currents on manifolds and metrics on curved spaces, enabling symmetry-preserving regularization in geometric analysis.

Contribution

It introduces new equivariant smoothing methods for currents and metrics, extending regularization processes to spaces with symmetry and bounded curvature.

Findings

Successfully implements equivariant smoothing of currents.

Extends smoothing operators to metric spaces with bounded curvature.

Preserves symmetries in regularization processes.

Abstract

We introduce actions of a compact Lie group in two regularization processes: in De Rham's approximation process of currents on a smooth manifold by smooth currents, and in a smoothing operator of Riemannian metrics of metric spaces with bounded curvature.