Normed spaces using intrinsically Lipschitz sections and Extension Theorem for the intrinsically H\"older sections

TL;DR

This paper introduces new norms based on intrinsically Lipschitz sections and extends a theorem for intrinsically Hölder sections to a broader target space, enhancing the theoretical framework in geometric analysis.

Contribution

It defines two new norms on intrinsically Lipschitz sections and generalizes an extension theorem for intrinsically Hölder sections to a product space target.

Findings

Defined two norms on intrinsically Lipschitz sections

Generalized extension theorem to target spaces of the form Y×R^s

Enhanced understanding of the structure of intrinsically Hölder sections

Abstract

The purpose of this article is twofold: first of all, we want to define two norms using the space of intrinsically Lipschitz sections. On the other hand, we want to generalize an Extension Theorem proved by the author in the context of the intrinsically H\"older sections with target a topological space $Y.$ Here our target will be $Y\times \R^s$ with $s \geq 1$ instead of $Y.$