Measures of Symmetry for Convex Sets and Stability

Gabor Toth is Chair of the Department of Mathematical Sciences at Rutgers University, Camden. His research interests include harmonic maps and minimal immersions and convex geometry. He is the author of Glimpses of Algebra and Geometry, as well as Finite Möbius Groups, Spherical Minimal Immersions, and Moduli.

• First Things First on Convex Sets.- Affine Diameters and the Critical Set.- Measures of Stability and Symmetry.- Mean Minkowski Measures.

"This is a graduate-level textbook on convex geometry in finite-dimensional Euclidean spaces, which has some interesting special features. ... Each chapter has illustrating figures and concludes with exercises ... . The book has a surprising appendix, where certain of the symmetry measures are applied to convex bodies ... . This book is an unconventional introduction to convexity, full of appealing intuitive geometry; it may equally well serve the beginner and the experienced researcher in the field." (Rolf Schneider, zbMATH 1335.52002, 2016)