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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

## Combinatorics: Ancient and Modern

*Robin Wilson and John J. Watkins (eds)*

- Published in print:
- 2013
- Published Online:
- September 2013
- ISBN:
- 9780199656592
- eISBN:
- 9780191748059
- Item type:
- book

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199656592.001.0001
- Subject:
- Mathematics, Combinatorics / Graph Theory / Discrete Mathematics, History of Mathematics

The history of mathematics is a well-studied and vibrant area of research, with books and scholarly articles published on various aspects of the subject. Yet, the history of combinatorics seems to ... 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 ^{R}3, 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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