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
• Títulos paralelos:
  • Restricción y decaimiento para hipersuperficies planas
• Enlaces
  • Texto completo
• 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.