The Proof of restriction conjecture In $\mathbb{R}^{3}$

Hoyoung Song

The Proof of restriction conjecture In $\mathbb{R}^{3}$

Classical Analysis and ODEs 2023-04-05 v2

Authors: Hoyoung Song

Abstract

If S is a smooth compact surface in $\mathbb{R}^{3}$ with strictly positive second fundamental form, and $E_S$ is the corresponding extension operator, then we prove that for all $p > 3$ , $\left\|E_S f\right\|_{L^p\left(\mathbb{R}^3\right)} \leq C(p, S)\|f\|_{L^{\infty}(S)}.$ The proof of restriction conjecture in $\mathbb{R}^{3}$ implies that Kakeya set conjecture is true when n=3.

Keywords

conjectures and proofs bound

Cite

@article{arxiv.2304.01092,
  title  = {The Proof of restriction conjecture In $\mathbb{R}^{3}$},
  author = {Hoyoung Song},
  journal= {arXiv preprint arXiv:2304.01092},
  year   = {2023}
}

Comments

There is an error for Lemma 3.1. There should be more condition so I think I should withdraw this article and my paper. It is famous problem, so withdrawing is necessary

The Proof of restriction conjecture In $\mathbb{R}^{3}$

Abstract

Keywords

Cite

Comments

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