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The non-manifold part

Friedhelm Waldhausen, Bjørn Jahren, and John Rognes

in Spaces of PL Manifolds and Categories of Simple Maps (AM-186)

Published in print:
2013
Published Online:
October 2017
ISBN:
9780691157757
eISBN:
9781400846528
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691157757.003.0004
Subject:
Mathematics, Geometry / Topology

Abstract and Keywords to be supplied.


Areas, Angles, and Polyhedra

Glen Van Brummelen

in Heavenly Mathematics: The Forgotten Art of Spherical Trigonometry

Published in print:
2017
Published Online:
May 2018
ISBN:
9780691175997
eISBN:
9781400844807
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691175997.003.0007
Subject:
Mathematics, History of Mathematics

This chapter explains how to find the area of an angle or polyhedron. It begins with a discussion of how to determine the area of a spherical triangle or polygon. The formula for the area of a ... More


Introducing Graphs

Arthur Benjamin, Gary Chartrand, and Ping Zhang

in The Fascinating World of Graph Theory

Published in print:
2017
Published Online:
May 2018
ISBN:
9780691175638
eISBN:
9781400852000
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691175638.003.0001
Subject:
Mathematics, Applied Mathematics

This chapter provides an introduction to graphs, a mathematical structure for visualizing, analyzing, and generalizing a situation or problem. It first consider four problems that have a distinct ... More


Drawing Graphs

Arthur Benjamin, Gary Chartrand, and Ping Zhang

in The Fascinating World of Graph Theory

Published in print:
2017
Published Online:
May 2018
ISBN:
9780691175638
eISBN:
9781400852000
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691175638.003.0010
Subject:
Mathematics, Applied Mathematics

This chapter considers the concept of planar graph and its underlying theory. It begins with a discussion of the Three Houses and Three Utilities Problem and how it can be represented by a graph. It ... More


Problems of Harmonic Analysis Related to Finite-Type Hypersurfaces in R3, and Newton Polyhedra Detlef Müller

Charles Fefferman, Alexandru D. Ionescu, D. H. Phong, Stephen Wainger, Charles Fefferman, Alexandru D. Ionescu, D. H. Phong, and Stephen Wainger (eds)

in Advances in Analysis: The Legacy of Elias M. Stein

Published in print:
2014
Published Online:
October 2017
ISBN:
9780691159416
eISBN:
9781400848935
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691159416.003.0013
Subject:
Mathematics, Numerical Analysis

This chapter presents three sets of problems and explains how these questions can be answered in an (almost) complete way in terms of Newton polyhedra associated to the given surface S (here, a ... More


Wright-Fisher Geometry

Charles L. Epstein and Rafe1 Mazzeo

in Degenerate Diffusion Operators Arising in Population Biology (AM-185)

Published in print:
2013
Published Online:
October 2017
ISBN:
9780691157122
eISBN:
9781400846108
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691157122.003.0002
Subject:
Mathematics, Probability / Statistics

This chapter introduces the geometric preliminaries needed to analyze generalized Kimura diffusions, with particular emphasis on Wright–Fisher geometry. It begins with a discussion of the natural ... More


Introduction

Isroil A. Ikromov, Detlef Müller, 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/9780691170541.003.0001
Subject:
Mathematics, Geometry / Topology

This chapter discusses the Fourier restriction. The Fourier restriction problem presents one important instance of a wide circle of related problems, such as the boundedness properties of Bochner ... 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


Proofs of Propositions 1.7 and 1.17

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/9780691170541.003.0009
Subject:
Mathematics, Geometry / Topology

This chapter showcases the remaining proofs of two results from the first chapter. It turns to the first of these results, based on a proposition made Chapter 1, on the characterization of linearly ... More


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