Jump to ContentJump to Main Navigation
Random Geometric Graphs$
Users without a subscription are not able to see the full content.

Mathew Penrose

Print publication date: 2003

Print ISBN-13: 9780198506263

Published to Oxford Scholarship Online: September 2007

DOI: 10.1093/acprof:oso/9780198506263.001.0001

Show Summary Details
Page of

PRINTED FROM OXFORD SCHOLARSHIP ONLINE (www.oxfordscholarship.com). (c) Copyright Oxford University Press, 2019. All Rights Reserved. An individual user may print out a PDF of a single chapter of a monograph in OSO for personal use. date: 15 October 2019

GEOMETRICAL INGREDIENTS

GEOMETRICAL INGREDIENTS

Chapter:
(p.95) 5 GEOMETRICAL INGREDIENTS
Source:
Random Geometric Graphs
Author(s):

Mathew Penrose (Contributor Webpage)

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780198506263.003.0005

This chapter contains some well-known deterministic geometric results for use in subsequent chapters. The Lebesgue density theorem is stated along with some of its consequences concerned with finding disjoint balls of high or low volume. Bounds are given for the covering and packing numbers of a compact (d-1)-submanifold in d-space. The Brunn-Minkowski inequality is stated and some of its consequences are derived, namely an isoperimetric inequality in the square and an isodiametric inequality. A lower bound is given for the volume of the difference between a shifted compact set and the original set.

Keywords:   geometric results, Lebesgue density theorem, Brunn-Minkowski inequality, isoperimetric inequality, isodiametric inequality, submanifold

Oxford Scholarship Online requires a subscription or purchase to access the full text of books within the service. Public users can however freely search the site and view the abstracts and keywords for each book and chapter.

Please, subscribe or login to access full text content.

If you think you should have access to this title, please contact your librarian.

To troubleshoot, please check our FAQs , and if you can't find the answer there, please contact us .