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arXiv · 2602.07431

Generalised lower Assouad-type dimensions and their interpolations

Haipeng Chen·Wen Wang
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Abstract

This paper investigates the analytic and structural properties of the $\phi$-lower Assouad dimension, a generalized notion extending the lower Assouad dimension. We establish the equivalence of $\phi$-lower Assouad dimensions with respect to the dimension functions, prove analytic properties related to the regularity of the $\phi$-lower dimension, and analyse the role of rate windows in this context. Furthermore, we explore both positive and negative interpolation properties of the $\phi$-lower dimension by presenting corresponding theorems that delineate these behaviors.

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Haipeng Chen, Wen Wang. 2026-02-07. Generalised lower Assouad-type dimensions and their interpolations. https://arxiv.org/abs/2602.07431

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