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INICIO | 24 de mayo 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
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Equipo DML-E
Instituto de Ciencias Matemáticas (ICMAT - CSIC)