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Restriction for Surfaces with Linear Height below 2

Isroil A. Ikromov and Detlef Müller

in Fourier Restriction for Hypersurfaces in Three Dimensions and Newton Polyhedra (AM-194)

Published in print:
2016
Published Online:
October 2017
ISBN:
9780691170541
eISBN:
9781400881246
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691170541.003.0004
Subject:
Mathematics, Geometry / Topology

This chapter studies the case where hsubscript lin(φ‎) < 2. It first performs a dyadic decomposition of a domain introduced in the previous chapter and the corresponding measure dμ‎superscript Greek ... More


The Case When hlin(φ‎) ≥ 2: Preparatory Results

Isroil A. Ikromov and Detlef Müller

in Fourier Restriction for Hypersurfaces in Three Dimensions and Newton Polyhedra (AM-194)

Published in print:
2016
Published Online:
October 2017
ISBN:
9780691170541
eISBN:
9781400881246
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691170541.003.0006
Subject:
Mathematics, Geometry / Topology

This chapter turns to the case where hsubscript lin(φ‎) ≥ 2. In a first step, the chapter performs a decomposition of the remaining piece Ssubscript Greek small letter psi of the surface S. Then, in ... More


The Remaining Cases Where m = 2 and B = 3 or B = 4

Isroil A. Ikromov and Detlef Müller

in Fourier Restriction for Hypersurfaces in Three Dimensions and Newton Polyhedra (AM-194)

Published in print:
2016
Published Online:
October 2017
ISBN:
9780691170541
eISBN:
9781400881246
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691170541.003.0008
Subject:
Mathematics, Geometry / Topology

This chapter discusses the remaining cases for l = 1. With the same basic approach as in Chapter 5, the chapter again performs an additional dyadic frequency domain decomposition related to the ... More


Reduction to Restriction Estimates near the Principal Root Jet

Isroil A. Ikromov and Detlef Müller

in Fourier Restriction for Hypersurfaces in Three Dimensions and Newton Polyhedra (AM-194)

Published in print:
2016
Published Online:
October 2017
ISBN:
9780691170541
eISBN:
9781400881246
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691170541.003.0003
Subject:
Mathematics, Geometry / Topology

This chapter shows that one may reduce the desired Fourier restriction estimate to a piece Ssubscript Greek small letter psi of the surface S lying above a small, “horn-shaped” neighborhood ... More


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