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Rolf Georg Schneider (born 17 March 1940, Hagen, Germany) [1] is a mathematician. Schneider is a professor emeritus at the University of Freiburg. His main research interests are convex geometry and stochastic geometry.
Rolf Schneider: On a formula for the volume of polytopes. In: Geometric Aspects of Functional Analysis (Israel Seminar 2017-2019), vol. II, pp. 335-345, Lecture Notes Math. 2266 , Springer, 2020.
Review of the first edition:‘Professor Schneider's book is the first comprehensive account of the Brunn-Minkowski theory and will immediately become the standard reference for the Aleksandrov-Fenchel inequalities and the current knowledge concerning the cases of equality and estimates of their stability.
- Rolf Schneider
- 1993
- Preface to the second edition
- General hints to the literature
- Conventions and notation
- Conventions and notation
- = ∈ R = α
- I∞ A (x) :
- 0 if P(x) is false. Conventions and notation
- Conventions and notation
- k ffi
- R n S
- K × R → K
- GeneratedCaptionsTabForHeroSec
Wie machen wirs, daß alles frisch und neu Und mit Bedeutung auch gef ̈allig sei? Goethe, Faust I The past 20 years have seen considerable progress and lively activity in various di erent areas of convex geometry. In order that this book still meet its intended ff purpose, it had to be updated and expanded. It remains the aim of the book to serve th...
This book treats convex bodies with a special view to its classical part known as Brunn–Minkowski theory. To give the reader a wider picture of convex geometry, we collect here a list of textbooks and monographs, roughly ordered by category and year of publication. Each of the books listed under ‘General’ has parts which can serve as an introductio...
Here we fix our notation and collect some basic definitions. We shall work in n-dimensional real Euclidean vector space, Rn, with origin o, standard scalar product , , and induced norm . We do not distinguish formally between the vector space n · | · | and its corresponding a ne space, although our alternating use of the words
for a half-open segment, both with endpoints x, y. n For A, B and we define ⊂ R λ ∈ R B : a b : B = + A, b ∈ ∈ , λA : λa : a A = ∈ , and we write A for ( 1)A, A B for A ( B) and A x for A x , where x n. − − − + − + + { } ∈ The set A B is written A B and called the direct sum of A and B if A and B R are + ⊕ contained in complementary a ne subspaces ...
with u n o and α ; here Hu,α H if and only if ( , β) (λu, λα)
= for A. ∞ A, ∈ n ∈ R \ If P(x) is an assertion about the elements x of a set A, we use also the notation
xxi The following metric notions will be used. For x, y n and ∈ R ∅ the distance between x and y and A n, x y is ⊂ R | −| d(A x) : inf x a : a A , = | −| ∈ is the distance of x from A. For a bounded set A n, ∅ ⊂ R diam A : sup x y : x, y A = | −| ∈ is the diameter of A. It is also denoted by D(A). We write
itself, and it is a rotation if it is an isometry fixing the origin. Every rigid motion is the composition of a rotation and a translation. A rigid motion is called proper if it preserves the orientation of n; otherwise it is called improper. A rotation of n is R linear map; it preserves the scalar product and can be represented, with respect to an...
is the image of under some isometry, it is clear (and common practice without R mention) that R all notions and results that have been established for k and are invari-ant under isometries can be applied in E; similarly for a R ne-invariant notions and ffi results. R can arise). The following notational conventions will be useful at several places....
Very often, mappings of the type f : M will occur where is some class
of subsets of n. In this case we usually abbreviate, for fixed K , the function f(K, ) : n R ∈ K M by fK. · R → We wish to point out that in definitions the word ‘if’ is always understood as ‘if and only if’. Finally, a remark about citations. When we list several publications consecutively, particularly in the chapter notes, we usually order them ...
A comprehensive introduction to convex bodies and their applications, with full proofs and references. The book covers mixed volumes, valuations, extensions, and constructions and inequalities, and is part of the Encyclopedia of Mathematics and Its Applications series.
Rolf Schneider. presents the fundamentals for recent applications of convex cones and describes selected examples. combines the active fields of convex geometry and stochastic geometry. addresses beginners as well as advanced researchers. Part of the book series: Lecture Notes in Mathematics (LNM, volume 2319) 7737 Accesses. 1 Citations.
A comprehensive monograph on convex bodies and their applications, with a focus on the Brunn–Minkowski theory and its extensions. The author is a professor of mathematics at Albert-Ludwigs-Universität Freiburg, Germany.
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Rolf Schneider. Wolfgang Weil. First book since Santalo's classic 1976 to combine stochastic geometry and integral geometry. It presents rigorous foundations of the models of stochastic geometry as well as of the tools from integral geometry, and supplies with clear, complete, and comprehensible proofs of the major results.
