A Schur's theorem via a monotonicity and the expansion module
Differential Geometry
2023-02-22 v2
Abstract
In this paper we present a monotonicity which extends a classical theorem of A. Schur comparing the chord length of a convex plane curve with a space curve of smaller curvature. We also prove a Schur's Theorem for spherical curves, which extends the Cauchy's Arm Lemma.
Keywords
Cite
@article{arxiv.2301.03732,
title = {A Schur's theorem via a monotonicity and the expansion module},
author = {Lei Ni},
journal= {arXiv preprint arXiv:2301.03732},
year = {2023}
}