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arXiv · 2610.25907

The $(n-2)$-linear restriction estimate in $\mathbb R^n$

Faruk Temur
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Abstract

We present a proof for the $(n-2)$-linear extension estimate for curved surfaces in $\mathbb{R}^n$, $n\ge5$, 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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Faruk Temur. 2026-10-19. The $(n-2)$-linear restriction estimate in $\mathbb R^n$. https://arxiv.org/abs/2610.25907

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