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PreprintarXiv licencearXiv

The square function estimates for cones in arbitrary dimensions and elliptic quadrics

  • Faruk Temur
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Abstract

We demonstrate that the square function estimate for the light cone in Rd, d≥3, at the exponent p=2(d−1)/(d−2), with loss [log(2R)]5/p can be deduced from local-smoothing and auxiliary-energy statements in the October 25, 2026 OpenAI manuscript. Exact affine sections preserve these logarithmic bounds and give corresponding estimates for spheres, ellipsoids, elliptic paraboloids, and compact patches of two-sheet elliptic hyperboloids in Rd−1.

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Cite

BibTeXRIS
BibTeX
@misc{temur2026square,
  title = {{The square function estimates for cones in arbitrary dimensions and elliptic quadrics}},
  author = {Faruk Temur},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2611.07085},
  eprint = {2611.07085},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2611.07085},
}
RIS
TY  - UNPB
TI  - The square function estimates for cones in arbitrary dimensions and elliptic quadrics
AU  - Faruk Temur
PY  - 2026
DA  - 2026/11/04
PB  - arXiv
DO  - 10.48550/arxiv.2611.07085
UR  - https://arxiv.org/abs/2611.07085
AB  - We demonstrate that the square function estimate for the light cone in R^d, d≥3, at the exponent p=2(d−1)/(d−2), with loss [log(2R)]^5/p can be deduced from local-smoothing and auxiliary-energy statements in the October 25, 2026 OpenAI manuscript. Exact affine sections preserve these logarithmic bounds and give corresponding estimates for spheres, ellipsoids, elliptic paraboloids, and compact patches of two-sheet elliptic hyperboloids in R^d−1.
ER  -