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arXiv · 2609.21535

A diameter gap for irreducible compact symmetric spaces of fixed rank

Zhiqi Chen·Shaoqiang Deng·Hui Zhang
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Abstract

For every positive integer $r$, we prove that positive-diameter isometric quotients of simply connected irreducible compact Riemannian symmetric spaces of rank $r$ have a uniform positive lower bound on their normalized diameter. The bound is independent of dimension and of the acting group, which may be disconnected. The rank-one case is due to Gorodski, Lange, Lytchak, and Mendes \cite{GLLM}. For the higher-rank Grassmannian families, we construct nonconstant invariant functions of bounded trigonometric degree. The real and complex cases use a moment map argument. The quaternionic case uses a quartic rigidity argument and the classification of compact quaternionic symmetric spaces.

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Zhiqi Chen, Shaoqiang Deng, Hui Zhang. 2026-09-18. A diameter gap for irreducible compact symmetric spaces of fixed rank. https://arxiv.org/abs/2609.21535

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