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PreprintCC BY 4.0arXiv

The (n−1)-linear restriction estimate in ℝn with degenerate curvature

  • Ioan Bejenaru
  • Tiklung Chan
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Abstract

We revisit the (n−1)-linear restriction estimate in ℝn proved by the first author in \cite{Be-6} and refine the result in the case when the curvature assumptions contain small parameters. The standard Lp estimate is replaced by a more complex norm/quasi-norm of type ℓp L/2n−2 which reflects the geometry of wave packet propagation and the degenerate curvature assumptions. The primary motivation for this work stems from a concrete application to the study of the quadratic nonlinear Schrödinger equation in ℝ3+1, which is done in a companion paper \cite{BeBoCh}.

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Cite

BibTeXRIS
BibTeX
@misc{bejenaru2026n1linear,
  title = {{The $(n-1)$-linear restriction estimate in $\mathbbR^n$ with degenerate curvature}},
  author = {Ioan Bejenaru and Tiklung Chan},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.20909},
  eprint = {2610.20909},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.20909},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - The (n−1)-linear restriction estimate in ℝ^n with degenerate curvature
AU  - Ioan Bejenaru
AU  - Tiklung Chan
PY  - 2026
DA  - 2026/10/14
PB  - arXiv
DO  - 10.48550/arxiv.2610.20909
UR  - https://arxiv.org/abs/2610.20909
AB  - We revisit the (n−1)-linear restriction estimate in ℝ^n proved by the first author in \cite{Be-6} and refine the result in the case when the curvature assumptions contain small parameters. The standard L^p estimate is replaced by a more complex norm/quasi-norm of type ℓ^p L^/2n−2 which reflects the geometry of wave packet propagation and the degenerate curvature assumptions. The primary motivation for this work stems from a concrete application to the study of the quadratic nonlinear Schrödinger equation in ℝ^3+1, which is done in a companion paper \cite{BeBoCh}.
ER  -