Projections of sets with optimal oracles onto $k$-planes
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866911574053093376 |
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| author | Fiedler, Jacob B. Jing, Zhifan |
| author_facet | Fiedler, Jacob B. Jing, Zhifan |
| contents | We prove a Kaufman-type exceptional set estimate for sets in $\mathbb{R}^n$ that have optimal oracles, a class of sets that strictly contains the analytic sets and sets with equal Hausdorff and packing dimension. As a consequence, we generalize the conditions under which Marstrand's projection theorem for $k$-planes is known to hold. Our proofs use effective methods, especially Kolmogorov complexity, and along the way, we introduce several new tools for studying the information content of elements of the Grassmannian. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_06119 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Projections of sets with optimal oracles onto $k$-planes Fiedler, Jacob B. Jing, Zhifan Classical Analysis and ODEs Logic 28A78, 28A80, 68Q30 We prove a Kaufman-type exceptional set estimate for sets in $\mathbb{R}^n$ that have optimal oracles, a class of sets that strictly contains the analytic sets and sets with equal Hausdorff and packing dimension. As a consequence, we generalize the conditions under which Marstrand's projection theorem for $k$-planes is known to hold. Our proofs use effective methods, especially Kolmogorov complexity, and along the way, we introduce several new tools for studying the information content of elements of the Grassmannian. |
| title | Projections of sets with optimal oracles onto $k$-planes |
| topic | Classical Analysis and ODEs Logic 28A78, 28A80, 68Q30 |
| url | https://arxiv.org/abs/2604.06119 |