Work

Sharp Projection Bounds for Intermediate Dimensions of Measures

Year: 2026

Type: preprint

Abstract: We prove sharp bounds for the upper and lower intermediate dimensions of orthogonal and radial projections of compactly supported measures. Both dimension functions are preserved almost everywhere when the quasi-Assouad dimension does not exceed the target dimension. We obtain exceptional-set estimates using the entire source dimension function, with sharpness for explicit families. We also construct a fixed measure whose projected dimension functions vary on open direction sets, even when all source dimensions lie below the target dimension.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2610.32808

Authors: Zang, Shengyang, Zhao, Yingyu, Zhao, Yunhao, Zhou, Chen

Institutions: Nankai University, University of Chinese Academy of Sciences, Tsinghua University, Zhejiang University of Technology

Language: English

Topic: Mathematical Dynamics and Fractals

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W7223651238

Cites: 13

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Related to: 10