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PreprintarXiv licencearXiv

Sharp Projection Bounds for Intermediate Dimensions of Measures

  • Shengyang Zang
  • Yingyu Zhao
  • Yunhao Zhao
  • Chen Zhou
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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.

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Cite

BibTeXRIS
BibTeX
@misc{zang2026sharp,
  title = {{Sharp Projection Bounds for Intermediate Dimensions of Measures}},
  author = {Shengyang Zang and Yingyu Zhao and Yunhao Zhao and Chen Zhou},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.32808},
  eprint = {2610.32808},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.32808},
}
RIS
TY  - UNPB
TI  - Sharp Projection Bounds for Intermediate Dimensions of Measures
AU  - Shengyang Zang
AU  - Yingyu Zhao
AU  - Yunhao Zhao
AU  - Chen Zhou
PY  - 2026
DA  - 2026/10/23
PB  - arXiv
DO  - 10.48550/arxiv.2610.32808
UR  - https://arxiv.org/abs/2610.32808
AB  - 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.
ER  -