Restriction and decay for flat hypersurfaces

• Autores: Anthony Carbery , Sarah Ziesler
• Localización: Publicacions matematiques, ISSN 0214-1493, Vol. 46, Nº 2, 2002, págs. 405-434
• Idioma: inglés
• DOI: 10.5565/publmat_46202_04
• Títulos paralelos:
  • Restricción y decaimiento para hipersuperficies planas
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• Resumen

  • In the first part we consider restriction theorems for hypersurfaces $\Gamma$ in ${\mathbf R}^n$, with the affine curvature $K_{\Gamma}^{1/(n+1)}$ introduced as a mitigating factor. Sjölin, [19], showed that there is a universal restriction theorem for all convex curves in ${\mathbf R}^2$. We show that in dimensions greater than two there is no analogous universal restriction theorem for hypersurfaces with non-negative curvature.