On the Action of Reparametrization Group on the Space of $L_k^p$-maps I

TL;DR

This paper proves that the reparametrization group acts properly on the space of $L_k^p$-maps, providing foundational understanding for the structure of these function spaces.

Contribution

It establishes the properness of the reparametrization group action on $L_k^p$-maps, a key step in analyzing their geometric and analytical properties.

Findings

Reparametrization group action is proper on $L_k^p$-maps.

Provides a foundation for further geometric analysis of $L_k^p$-spaces.

Enhances understanding of symmetry groups in functional analysis.

Abstract

We prove that the action of reparametrization group on the space of $L_k^p$-maps is proper, which is defined in this paper.