Presentación | Participantes | Bibliografía (DML-E) | Bibliografía adicional | Enlaces de interés | Otros proyectos DML | Ayuda
INICIO |
27 de julio de 2024
Restriction and decay for flat hypersurfaces.
| Título inglés | Restriction and decay for flat hypersurfaces. |
|---|---|
| Título español | Restricción y decaimiento para hipersuperficies planas. |
| Autor/es | Carbery, Anthony ; Ziesler, Sarah |
| Organización | Dep. Math. Statist. Univ. Edinburgh, Edimburgo, Reino Unido;Dep. Math. Comput. Sci. Dominican Univ., River Forest (Illinois), Estados Unidos |
| Revista | 0214-1493 |
| Publicación | 2002, 46 (2): 405-434, 28 Ref. |
| Tipo de documento | articulo |
| Idioma | Inglés |
| Resumen inglés | In the first part we consider restriction theorems for hypersurfaces Γ in Rn, with the affine curvature KΓ1/(n+1) introduced as a mitigating factor. Sjölin, [19], showed that there is a universal restriction theorem for all convex curves in R2. We show that in dimensions greater than two there is no analogous universal restriction theorem for hypersurfaces with non-negative curvature. In the second part we discuss decay estimates for the Fourier transform of the density KΓ1/2 supported on the surface and investigate the relationship between restriction and decay in this setting. It is well-known that restriction theorems follow from appropriate decay estimates; one would like to know whether restriction and decay are, in fact, equivalent. We show that this is not the case in two dimensions. We also go some way towards a classification of those curves/surfaces for which decay holds by giving some sufficient conditions and some necessary conditions for decay. |
| Clasificación UNESCO | 120213 |
| Palabras clave español | Hipersuperficies ; Curvatura ; Transformada de Fourier ; Restricción |
| Código MathReviews | MR1934361 |
 Acceso al artículo completo |
|