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The (n−2)-linear restriction estimate in ℝn
Abstract
We present a proof for the (n−2)-linear extension estimate for curved surfaces in ℝn, n≥5, at the local product exponent 2(n−1)/(n−2)2, with an arbitrarily small power loss. The hypotheses are transversality of the normals and nondegeneracy of the compressed shape operators on their common two-dimensional orthogonal complement. The argument combines polynomial partitioning, a descent through algebraic varieties, localized multilinear restriction, and positive packet-energy estimates.
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BibTeX
@misc{temur2026n2linear,
title = {{The $(n-2)$-linear restriction estimate in $\mathbb R^n$}},
author = {Faruk Temur},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.25907},
eprint = {2610.25907},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.25907},
}
RIS
TY - UNPB
TI - The (n−2)-linear restriction estimate in ℝ^n
AU - Faruk Temur
PY - 2026
DA - 2026/10/19
PB - arXiv
DO - 10.48550/arxiv.2610.25907
UR - https://arxiv.org/abs/2610.25907
AB - We present a proof for the (n−2)-linear extension estimate for curved surfaces in ℝ^n, n≥5, at the local product exponent 2(n−1)/(n−2)^2, with an arbitrarily small power loss. The hypotheses are transversality of the normals and nondegeneracy of the compressed shape operators on their common two-dimensional orthogonal complement. The argument combines polynomial partitioning, a descent through algebraic varieties, localized multilinear restriction, and positive packet-energy estimates.
ER -