A Schur's theorem via a monotonicity and the expansion module

2023/01/10 by Ni, Lei
#53A04 #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2301.03732

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.

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