Displaying similar documents to “On surfaces of general type with pg = q = 1, K2 = 3.”

Wolff's inequality for hypersurfaces.

Izabella Laba, Malabika Pramanik (2006)

Collectanea Mathematica

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We extend Wolff's "local smoothing" inequality to a wider class of not necessarily conical hypersurfaces of codimension 1. This class includes surfaces with nonvanishing curvature, as well as certain surfaces with more than one flat direction. An immediate consequence is the L-boundedness of the corresponding Fourier multiplier operators.

Five-gonal curves of genus nine.

Marc Coppens (2005)

Collectanea Mathematica

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Let C be a smooth 5-gonal curve of genus 9. Assume all linear systems g on C are of type I (i.e. they can be counted with multiplicity 1) and let m be the numer of linear systems g on C. The only possibilities are m=1; m=2; m=3 and m=6. Each of those possibilities occur.

On the Moser-Onofri and Prékopa-Leindler inequalities.

Alessandro Ghigi (2005)

Collectanea Mathematica

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Using elementary convexity arguments involving the Legendre transformation and the Prékopa-Leindler inequality, we prove the sharp Moser-Onofri inequality, which says that 1/16π ∫|∇φ|2 + 1/4π ∫ φ - log (1/4π ∫ eφ) ≥ 0 for any funcion φ ∈ C∞(S2).

A generalization of the Nikodym boundedness theorem.

Christopher Stuart (2007)

Collectanea Mathematica

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In this note an internal property of a ring of sets, named the Nested Partition Property, is shown to imply the Nikodym Property. A wide range of examples are shown to have this property.