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Convexity from the geometric point of view

Balestro, Vitor

eBook Birkhäuser <editore> 2024

Abstract

This text gives a comprehensive introduction to the “common core” of convex geometry. Basic concepts and tools which are present in all branches of that field are presented with a highly didactic approach. [...]
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Descrizione *Convexity from the geometric point of view / Vitor Balestro, Horst Martini, Ralph Teixeira. - Cham : Birkhäuser, 2024. - 1 testo elettronico (xix, 1184 p. : ill.)
ISBN E-Book 9783031505072
Collana Cornerstones
Primo Autore
Balestro, Vitor
Coautore
Martini, Horst
Teixeira, Ralph
Soggetti 01A60 - History of mathematics in the 20th century [MSC 2020]
11H06 - Lattices and convex bodies (number-theoretic aspects) [MSC 2020]
14M25 - Toric varieties, Newton polyhedra, Okounkov bodies [MSC 2020]
14P10 - Semialgebraic sets and related spaces [MSC 2020]
26A09 - Elementary functions [MSC 2020]
26A51 - Convexity of real functions in one variable, generalizations [MSC 2020]
26B25 - Convexity of real functions of several variables, generalizations [MSC 2020]
28A75 - Length, area, volume, other geometric measure theory [MSC 2020]
28A78 - Hausdorff and packing measures [MSC 2020]
32F17 - Other notions of convexity in relation to several complex variables [MSC 2020]
46B07 - Local theory of Banach spaces [MSC 2020]
46B20 - Geometry and structure of normed linear spaces [MSC 2020]
51M04 - Elementary problems in Euclidean geometries [MSC 2020]
51M05 - Euclidean geometries (general) and generalizations [MSC 2020]
51M16 - Inequalities and extremum problems in real or complex geometry [MSC 2020]
51M20 - Polyhedra and polytopes; regular figures, division of spaces [MSC 2020]
52A05 - Convex sets without dimension restrictions (aspects of convex geometry) [MSC 2020]
52A20 - Convex sets in $n$ dimensions (including convex hypersurfaces) [MSC 2020]
52A22 - Random convex sets and integral geometry (aspects of convex geometry) [MSC 2020]
52A30 - Variants of convex sets (star-shaped, ($m, n$)-convex, etc.) [MSC 2020]
52A35 - Helly-type theorems and geometric transversal theory [MSC 2020]
52A38 - Length, area, volume (aspects of convex geometry) [MSC 2020]
52A39 - Mixed volumes and related topics in convex geometry [MSC 2020]
52A40 - Inequalities and extremum problems involving convexity in convex geometry [MSC 2020]
52A41 - Convex functions and convex programs in convex geometry [MSC 2020]
52B11 - $n$-dimensional polytopes [MSC 2020]
52B12 - Special polytopes (linear programming, centrally symmetric, etc.) [MSC 2020]
52B20 - Lattice polytopes in convex geometry (including relations with commutative algebra and algebraic geometry) [MSC 2020]
52B45 - Dissections and valuations (Hilbert's third problem, etc.) [MSC 2020]
52B55 - Computational aspects related to convexity [MSC 2020]
52B70 - Polyhedral manifolds [MSC 2020]
52C07 - Lattices and convex bodies in $n$ dimensions (aspects of discrete geometry) [MSC 2020]
52C17 - Packing and covering in $n$ dimensions (aspects of discrete geometry) [MSC 2020]
52C22 - Tilings in $n$ dimensions (aspects of discrete geometry) [MSC 2020]
52C35 - Arrangements of points, flats, hyperplanes (aspects of discrete geometry) [MSC 2020]
53C60 - Global differential geometry of Finsler spaces and generalizations (areal metrics) [MSC 2020]
53C65 - Integral geometry; differential forms, currents, etc. [MSC 2020]
58B20 - Riemannian, Finsler and other geometric structures on infinite-dimensional manifolds [MSC 2020]
90C05 - Linear programming [MSC 2020]
90C25 - Convex programming [MSC 2020]
Parole chiave Affine position
Asymptotic Geometric Analysis
Convex Bodies
Convex Polytopes
Geometric Inequalities
Luogo pubblicazione Cham
Editori Birkhäuser <editore>
Anno pubblicazione 2024
Thesauri $n$-dimensional polytopes [MSC 2020]
01A60
11H06
14M25
14P10
26A09
26A51
26B25
28A75
28A78
32F17
46B07
46B20
51M04
51M05
51M16
51M20
52A05
52A20
52A22
52A30
52A35
52A38
52A39
52A40
52A41
52B11
52B12
52B20
52B45
52B55
52B70
52C07
52C17
52C22
52C35
53C60
53C65
58B20
90C05
90C25
Arrangements of points, flats, hyperplanes (aspects of discrete geometry) [MSC 2020]
Computational aspects related to convexity [MSC 2020]
Convex functions and convex programs in convex geometry [MSC 2020]
Convex programming [MSC 2020]
Convex sets in $n$ dimensions (including convex hypersurfaces) [MSC 2020]
Convex sets without dimension restrictions (aspects of convex geometry) [MSC 2020]
Convexity of real functions in one variable, generalizations [MSC 2020]
Convexity of real functions of several variables, generalizations [MSC 2020]
Dissections and valuations (Hilbert's third problem, etc.) [MSC 2020]
Elementary functions [MSC 2020]
Elementary problems in Euclidean geometries [MSC 2020]
Euclidean geometries (general) and generalizations [MSC 2020]
Geometry and structure of normed linear spaces [MSC 2020]
Global differential geometry of Finsler spaces and generalizations (areal metrics) [MSC 2020]
Hausdorff and packing measures [MSC 2020]
Helly-type theorems and geometric transversal theory [MSC 2020]
History of mathematics in the 20th century [MSC 2020]
Inequalities and extremum problems in real or complex geometry [MSC 2020]
Inequalities and extremum problems involving convexity in convex geometry [MSC 2020]
Integral geometry; differential forms, currents, etc. [MSC 2020]
Lattice polytopes in convex geometry (including relations with commutative algebra and algebraic geometry) [MSC 2020]
Lattices and convex bodies (number-theoretic aspects) [MSC 2020]
Lattices and convex bodies in $n$ dimensions (aspects of discrete geometry) [MSC 2020]
Length, area, volume (aspects of convex geometry) [MSC 2020]
Length, area, volume, other geometric measure theory [MSC 2020]
Linear programming [MSC 2020]
Local theory of Banach spaces [MSC 2020]
Mixed volumes and related topics in convex geometry [MSC 2020]
Other notions of convexity in relation to several complex variables [MSC 2020]
Packing and covering in $n$ dimensions (aspects of discrete geometry) [MSC 2020]
Polyhedra and polytopes; regular figures, division of spaces [MSC 2020]
Polyhedral manifolds [MSC 2020]
Random convex sets and integral geometry (aspects of convex geometry) [MSC 2020]
Riemannian, Finsler and other geometric structures on infinite-dimensional manifolds [MSC 2020]
Semialgebraic sets and related spaces [MSC 2020]
Special polytopes (linear programming, centrally symmetric, etc.) [MSC 2020]
Tilings in $n$ dimensions (aspects of discrete geometry) [MSC 2020]
Toric varieties, Newton polyhedra, Okounkov bodies [MSC 2020]
Variants of convex sets (star-shaped, ($m, n$)-convex, etc.) [MSC 2020]