Open AccessA note on the restriction theorem and geometry of hypersurfaces
Author(s) -
Fabio Nicola
Publication year - 2008
Publication title -
mathematica scandinavica
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.553
H-Index - 30
eISSN - 1903-1807
pISSN - 0025-5521
DOI - 10.7146/math.scand.a-15068
Subject(s) - hypersurface , mathematics , gaussian curvature , geometry , curvature , range (aeronautics) , mean curvature , mathematical analysis , pure mathematics , materials science , composite material
A necessary condition is established for the optimal $(L^p,L^2)$ restriction theorem to hold on a hypersurface $S$, in terms of its Gaussian curvature. For some classes of flat hypersurface we give sharp thresholds for the range of admissible exponents $p$, depending on the specific geometry.
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