# Measures of Symmetry for Convex Sets and Stability

This textbook treats two important and related matters in convex geometry: the quantification of symmetry of a convex set-measures of symmetry-and the degree to which convex sets that nearly minimize such measures of symmetry are themselves nearly symmetric-the phenomenon of stability. By gathering the subject's core ideas and highlights around Grunbaum's general notion of measure of symmetry, it paints a coherent picture of the subject, and guides the reader from the basics to the state-of-the-art. The exposition takes various paths to results in order to develop the reader's grasp of the unity of ideas, while interspersed remarks enrich the material with a behind-the-scenes view of corollaries and logical connections, alternative proofs, and allied results from the literature. Numerous illustrations elucidate definitions and key constructions, and over 70 exercises-with hints and references for the more difficult ones-test and sharpen the reader's comprehension. The presentation includes: a basic course covering foundational notions in convex geometry, the three pillars of the combinatorial theory the theorems of Caratheodory, Radon, and Helly, critical sets and Minkowski measure, the Minkowski-Radon inequality, and, to illustrate the general theory, a study of convex bodies of constant width; two proofs of F. John's ellipsoid theorem; a treatment of the stability of Minkowski measure, the Banach-Mazur metric, and Groemer's stability estimate for the Brunn-Minkowski inequality; important specializations of Grunbaum's abstract measure of symmetry, such as Winternitz measure, the Rogers-Shepard volume ratio, and Guo's Lp -Minkowski measure; a construction by the author of a new sequence of measures of symmetry, the kth mean Minkowski measure; and lastly, an intriguing application to the moduli space of certain distinguished maps from a Riemannian homogeneous space to spheres-illustrating the broad mathematical relevance of the book's subject.

View more

Number of Pages: 278
Format(s): Paperback - ISBN: 9783319237329
Publication Date:
Listed in: Algebraic geometry
Publisher: Springer International Publishing AG

Paperback

RRP: £54.99

Total: £46.45

Save: £8.54 per copy!

Currently out of stock

## Mumford-Tate Groups and Domains: Their Geometry and Arithmetic (AM-183)

### By Phillip Griffiths

Save £43.54 = £71.46

## Mumford-Tate Groups and Domains: Their Geometry and Arithmetic (AM-183)

### By Mark Green

Save £18.34 = £33.66

## Lectures on Algebraic Cycles

### By Spencer J. Bloch

Save £4.67 = £41.32

## Some Problems of Unlikely Intersections in Arithmetic and Geometry (AM-181)

### By Umberto Zannier

Save £18.34 = £33.66

## London Mathematical Society Lecture Note Series Motivic Integration and its Interactions with Model Theory and Non-Archimedean Geometry: Series Number 383: Volume 1

Save £5.19 = £45.81

## Latest from the blog

### Fantastic new recipe book from Sabrina Ghayour 'Sirocco'

Sabrina Ghayour's long awaited second recipe book Sirocco is out this month and is a great follow up to Persianna. Read article

### Ten Great Bedtime Reads from The Great British Bookshop and Aspace

We have teamed up with Aspace (www.aspace.co.uk) who create beautiful room for Children to bring you 10 great bedtime reads for your little ones. Read article

## Breaking book world news

Posted 09/06/2016

### Literary Event Focus June-Sept 2016

Posted 23/02/2015

### Bath Literature Festival Judges deem Wolf Hall as 'outstanding novel of our time'

Posted 19/02/2015

### NLT & Walker Books Launch Alex Rider 15th Anniversary Writing Competition for Schools

• @TheGBBookshop - 2 years ago

Lottery funding for dementia reading project £2m pledged for Reading Agency scheme to pair readers with dementia sufferers

@TheGBBookshop - 2 years ago

Harry Potter and the Cursed Child has held on to the number one spot for a sixth week #HarryPotter #CursedChild @littlebrown @pottermore

• @TheGBBookshop - 2 years ago

@thebookseller @MartinaCole @Jeffrey_Archer @Foyles

@TheGBBookshop - 2 years ago

Frith wins inaugural Klaus Flugge Prize for illustration t.co/U9P08h4XMG

• @TheGBBookshop - 3 years ago