Year: 2026
Type: preprint
Abstract: We prove that, for every positive integer $r$, the positive normalized diameters of isometric quotients of simply connected irreducible compact Riemannian symmetric spaces of rank $r$ have a uniform positive lower bound. The bound is independent of the dimension and of the acting group, which need not be connected. For the higher-dimensional Grassmannian families, we obtain an explicit bound for positive-dimensional acting groups by constructing nonconstant invariant functions of bounded trigonometric degree. The real and complex cases use moment maps. The quaternionic case follows from a quartic rigidity theorem proved by means of invariant four-forms and the classification of compact quaternionic symmetric spaces. We also give examples showing why the rank and the relative scales of product factors must be controlled.
Source: arXiv (Cornell University)
Authors: Chen, Zhiqi, Deng, Shaoqiang, Zhang, Hui
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7213948906