This article is cited in 1 paper

Graph comparison meets Alexandrov

N. D. Lebedeva^ab, A. M. Petrunin<sup>c

a</sup> Saint Petersburg State University
^b St. Petersburg Department of Steklov Mathematical Institute of Russian Academy of Sciences
^c Department of Mathematics, Pennsylvania State University

Abstract: Graph comparison is a certain type of condition on the metric space encoded by a finite graph. We show that each nontrivial graph comparison implies one of Alexandrov's comparisons. The proof gives a complete description of graphs with trivial graph comparisons.

Keywords: comparison theorems, Alexandrov's comparison, metric comparison.

UDC: 515.124

MSC: 35R30

Received: 12.02.2023
Revised: 09.03.2023
Accepted: 06.04.2023

DOI: 10.33048/smzh.2023.64.310

 English version: Siberian Mathematical Journal, 2023, 64:3, 624–628