000			01849nam a22002537a 4500
008			240708b |||||||| |||| 00| 0 eng d
020			_a9783030501792 (PB)
041			_aeng
080			_a514 _bHUG
100			_aHug, Daniel
245			_aLectures on Convex Geometry
260			_aCham _bSpringer _c2020
300			_axviii, 287p.
490			_aGraduate Texts in Mathematics _v286
504			_aIncludes References (281-284) and Index
505			_a 1. Convex Sets 2. Convex Functions 3. Brunn-Minkowski Theory 4. From Area Measures to Valuations 5. Integral-Geometric Formulas 6. Solutions of Selected Exercises
520			_aThis book provides a self-contained introduction to convex geometry in Euclidean space. After covering the basic concepts and results, it develops Brunn–Minkowski theory, with an exposition of mixed volumes, the Brunn–Minkowski inequality, and some of its consequences, including the isoperimetric inequality. Further central topics are then treated, such as surface area measures, projection functions, zonoids, and geometric valuations. Finally, an introduction to integral-geometric formulas in Euclidean space is provided. The numerous exercises and the supplementary material at the end of each section form an essential part of the book. Convexity is an elementary and natural concept. It plays a key role in many mathematical fields, including functional analysis, optimization, probability theory, and stochastic geometry. Paving the way to the more advanced and specialized literature, the material will be accessible to students in the third year and can be covered in one semester.
650			_aConvexity
650			_aConvex and Discrete Geometry
650			_aMeasure and Integration
690			_aMathematics
700			_aWeil, Wolfgang
942			_cBK
999			_c60510 _d60510