Flavors of GeometrySilvio Levy Cambridge University Press, 28. sep. 1997 - 194 sider Flavors of Geometry is a volume of lectures on four geometrically-influenced fields of mathematics that have experienced great development in recent years. Growing out of a series of introductory lectures given at the Mathematical Sciences Research Institute in January 1995 and January 1996, the book presents chapters by masters in their respective fields on hyperbolic geometry, dynamics in several complex variables, convex geometry, and volume estimation. Each lecture begins with a discussion of elementary concepts, examines the highlights of the field, and concludes with a look at more advanced material. The style and presentation of the chapters are clear and accessible, and most of the lectures are richly illustrated. Bibiliographies and indexes are included to encourage further reading on the topics discussed. |
Innhold
An Elementary Introduction to Modern Convex Geometry | 1 |
Hyperbolic Geometry | 59 |
Complex Dynamics in Several Variables | 117 |
Volume Estimates and Rapid Mixing | 151 |
| 183 | |
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algorithm angles approximation Bedford boundary bounded Brunn-Minkowski inequality combinatorial constant convex body convex geometry convex hull cube defined definition denote diffeomorphisms dimension disk distance entropy estimate Euclidean ball Figure fixed point Gaussian geodesic graph half-space model Hence Hénon map horseshoe map hyperbolic geometry hyperbolic space hyperboloid hyperboloid model inner product integral intersection isometry isoperimetric inequality John's Theorem Lecture Lemma length linear Lovász Math Mathematical matrix maximal ellipsoid maximal volume measure Milman Minkowski non-Euclidean geometry norm one-dimensional oracle orthogonal path periodic points plane polynomial polytope potential function Prékopa-Leindler inequality proof prove random walk result Riemannian metric Rn+1 segment sequence simplex slice Smillie space at infinity sphere stationary distribution stereographic projection subspace tangent theory topological unit ball unstable manifolds variables vector vertical voln volume ratio ән
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Side 177 - I. Barany and Z. Fiiredi. Computing the volume is difficult. Discrete Comput. Geom., 2:319-326, 1987.