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Schneider R. — Convex Bodies: The Brunn-Minkowski Theory
Schneider R. — Convex Bodies: The Brunn-Minkowski Theory

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Название: Convex Bodies: The Brunn-Minkowski Theory

Автор: Schneider R.

Аннотация:

At the heart of this monograph is the Brunn-Minkowski theory. It can be used to great effect in studying such ideas as volume and surface area and the generalizations of these. In particular the notions of mixed volume and mixed area arise naturally and the fundamental inequalities that are satisfied by mixed volumes are considered in detail. The author presents a comprehensive introduction to convex bodies and gives full proofs for some deeper theorems which have never previously been brought together. Many hints and pointers to connections with other fields are given, and an exhaustive reference list is included.


Язык: en

Рубрика: Математика/Геометрия и топология/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1993

Количество страниц: 490

Добавлена в каталог: 16.04.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$(K_1, \ldots, K_{n-1})$-extreme vector      76
$L_p$ metric      59
Abstract, convex cone      42
Abstract, Steiner point      178
Adapted, one convex body to another      374
Additive function      173
Affine combination      x
Affine hull      x
Affine isoperimetric inequality      419
Affine quermassintegral      387
Affine surface area      419
Affinely independent points      x
Ahrens, I.      3.1
Aleksandrov — Fenchel inequality      327
Aleksandrov — Fenchel — Jessen theorem      400 407
Aleksandrov, A.D.      1.5 1.7 2.2 2.4 2.5 3.5 4.2 4.3 4.6 5.1—5.3 6.2—6.6 6.8 7.1 7.2 Appendix
Alexander, R.      3.5
Alfsen, E.M.      1.4
Allendoerfer, C.B.      4.2
Ambartzumian, R.V.      3.5
Anderson, R.D.      2.2
Anikonov, Ju. E.      Appendix
Approximable convex body      162
Area measure      203
Area measure of order m      207
Area measure, mixed      274
Arnold, R.      5.4
Arrow, K.J.      3.1
Artstein, Z.      3.1
Ash, R.B.      4.1
Asplund, E.      1.5 2.1
Associated bodies      140
Assouad, P.      3.5
Asymmetry class      156
Baddeley, A.J.      4.4
Baebler, F.      6.2
Bair, J.      1.3 1.4 3.1 3.2
Baire space      119
Ball, K.      7.4
Banchoff, T.F.      4.4
Bandle, C.      6.2
Bandt, Ch.      1.8
Bangert, V.      1.5
Baniegnic, R.      1.8
Baraki, G.      1.8
Barthel, W      6.1 6.2
Barycentre function      21
Batson, R.G.      14
Bauer, H.      1.4 4.1
Baum, D.      1.7
Beer, G.A.      1.8
Bensimon, D      2.1
Benson, D.C.      6.2
Berg, Ch.      3.3 3.4 4.3 Appendix
Bernstein, D.N.      6.3
Berwald, L.      4.5
Besicovitch, A.S.      2.2 2.3
Betke, U.      3.5 4.2 4.5 5.3 6.2 7.4
Bettinger, W.      6.2
Bieberbach inequality      318
Bieberbach, L.      6.2
Biiranv, I.      2.3 2.6 7.1
Bing, R.H.      2.3
Bjorck, G.      2.1
Blackwell, D      3.5
Blaschke diagram      322
Blaschke diagram, Hausdorff metric      58
Blaschke diagram, Santalo inequality      387 421 425
Blaschke selection theorem      50
Blaschke sum      394
Blaschke symmetrization      165
Blaschke's rolling theorem      150
Blaschke, W.      1.8 2.5 3.2 3.3 3.5 4.3 4.5 5.3 5.4 6.1 6.2 6.4 7.1 7.4 Appendix
Blind, R.      7.2
Blumenthal, L.M.      1.8
Bocek, L.      6.2
Body of constant width      128
Bohm, J.      3.4
Bokowski, J.      2.4 4.5 5.3 6.2
Bol, G.      3.1 6.2 6.5—6.7 Appendix
Bolker, E.D.      3.5
Boltjanski, W.G.      3.5 6.5
Bonnesen, T.      1.7 2.2 3.1 3.3 4.3 5.1 5.3 5.4 6.1 6.2 6.4 6.7 7.1 7.3
Bonnesen-style inequalities      323
Bonnice, W.      1.3
Boolean model      256
Boroczky, K.      7.1
Borwein, J.M.      3.1
Bose, R.C.      5.4
Botts, T.      1.2
Bourbaki, N.      1.3 1.4 2.1 2.2
Bourgain, J.      3.3 3.5 6.1 6.2 7.2 7.4 Appendix
Brascamp, H.J.      6.1
Brehm, U.      4.4
Brondsted, A.      1.4 2.2 2.4 3.4
Bronshtein, E.M.      1.8 2.1 3.2 7.1
Brooks, J.N.      3.2
Brown, A.L.      2.1
Brunn — Minkowski inequality      309
Brunn — Minkowski inequality, extended      383
Brunn — Minkowski theorem      309
Brunn — Minkowski theorem, general      339
Brunn, H.      6.1
Budach, L.      4.4
Buldygin, V. V      6.1
Bunt, L.N.H.      1.2
Burago, Ju, D      1.2 1.3 6.1—6.3
Burckhardt, J.J.      3.5
Burton, G.R.      2.1 3.2 3.5 4.5
Busemann intersection inequality      417
Busemann — Petty centroid inequality      418
Busemann's theorem      316
Busemann, H.      1.5 2.5 4.6 6.1—6.3 6.8 7.1 7.2 7.4
Campi, S.      7.2 7.4 Appendix
Canal class      377
CAP      81
Cap-body      76
Cap-covering theorem      81 84
Caratheodory's theorem      3
Caratheodory, C      11
Cassels, J.W. S.      3.1
Cauchy's surface area formula      295
cc-hyperspace      57
Centred convex body      383
Centroid body      417
Chakerian, G.D.      3.1 3.5 6.2 6.5 7.1—7.4
Chebyshev set      11 67
Chebyshev subspace      94
Cheeger, J.      4.4
Chemoff, P.R.      Appendix
Cheng, S.-Y.      7.1
Chern, S.S.      2.5 4.5 5.3 7.2
Choquet theory      20
Choquet, G.      1.4 2.1 3.5
Christoffel's problem      216 218
Christoffel, E. B      4.3
Cieslak, W.      Appendix
Circumball      129
Circumradius      129
Clack, R.      7.4
Class asymmetry      156
Class canal      377
Class, universal approximating      162
Closed convex function      35
Closed convex hull      6
Closed halfspace      xi
Closed segment      x
Closing of set A by set B      138
Coifman, R.R.      Appendix
Collier, J.B.      2.1
Combination      1
Combination, affine      x
Combination, convex      1
Combination, linear      x
Combination, positive      2
Concave function      21
Conditionally positive definite function      194
Cone      80
Cone, convex      1
Cone, convex, abstract      42
Cone, convex, normal      70
Cone, convex, projection      70
Cone, convex, recession      17
Cone, convex, touching      74
Conjugate function      36
Contact measure      260
Convex body      8
Convex body, adapted      347
Convex body, approximable by a class      162
Convex body, centred      383
Convex body, decomposable      150
Convex body, determined by closed set      321 343
Convex body, equivalent by dilatation      383
Convex body, freely rolling      150
Convex body, freely sliding      143
Convex body, indecomposable      150 157 172
Convex body, irreducible      141 156
Convex body, k-curved      121
Convex body, normalized      150
Convex body, reducible      141 156
Convex body, stable      67
Convex body, strictly convex      77
Convex body, typical      119
Convex cone      1
Convex function      21
Convex hull      2
Convex ring      175
Convex set      1
Convex set, continuous      46
Convexity number      225
Corson, H.H.      2.1
Coxeter, H.S. M.      3.5
Cressie, N.      3.1
Critical set      141
Crofton's intersection formula      235
Curtis, D.W.      1.8
Curvature      104
Curvature centroid      305
Curvature function      419
Curvature image      420
Curvature measure      203
Curvature measure, generalized      202
Curvature, Gauss — Kronecker      106
Curvature, integral of mean      216
Curvature, Jessen radius of      117
Curvature, lower      104
Curvature, lower radius of      104
Curvature, mean      106
Curvature, principal      105
Curvature, principal radii of      108
Curvature, specific      269
Curvature, upper      104
Curvature, upper radius of      104
Curved convex body      121
Czipszer, J.      6.5
Dalla, L.      2.1
Danzer, L.      1.1 1.3
Das Gupta, S      6.1
Davis, C.      1.3
Davy, P.J.      4.5 5.4
Debrunner, H.      5.3
Debs, G.      2.1
Decomposable convex body      150
Defined locally, measure      206
Deicke, A.      7.4
Delgado, J.A.      3.2
Determined by closed set, convex body      321 343
Diameter      xi
Dierolf, P.      1.8
Difference body      127 409
Difference body inequality      409
Dilatation      xii 138
DIMENSION      7
Dinghas, A.      1.8 3.1 5.3 6.1 6.2 6.5 6.7 Appendix
Direct sum      xi
Direct summand      142
Directly indecomposable      142
Diskant, V.I.      6.1 6.2 6.4 6.5 6.7 7.2
Distance      xi
Dor, L.E.      3.5
Dresevic, M.      1.8
Dual affine quermassintegral      387
Dual cone      34
Dual mixed volume      385
Dual quermassintegral      386
Dubins, L.E.      1.4
Dubois, C      3.1
Dudley, R.      1.5 1.8
Dupin indicatrix      116
Dupin, Ch,      7.4
Duporcq, E.      5.4
Dziechcinska-Halamoda, Z.      3.1
Eckhoff, J.      1.1 3.4 4.5
Edelstein, M      2.1 3.1
EDGE      96
Effective domain      22
Efimov, N.W.      6.6
Eggleston, H.G.      2.1 6.2 7.3
Egorychev, G.P.      6.8
Eifler, L.Q.      2.1
Ekeland, I.      3.1
Endomorphism      170
Envelope      67
Epelman, M.S.      2.2
Epigraph      22
Equivalent by dilatation, convex bodies      383
Equivalent by telescoping, convex bodies      380
Equivariant map      166
Equivariant under rigid motions, Steiner point      43
Erosion      138
Euler characteristic      175
Euler point      116
Euler relation      179
Euler's theorem      106
Euler-type relation      180
Even measure      183
Ewald, G.      1.7 2.3 3.1 3.2 6.6
Exponent of entropy      60
Exposed      65
Exposed face      63 65
Exposed normal vector      74
Exposed point      19 65
Exposed r-skeleton      65
Exposed support plane      74
Extended Brunn — Minkowski inequality      383
Extended convex ring      256
Extended exterior normal vector      11 70
External angle      100
Extreme normal vector      74 76
Extreme point      18 65
Extreme ray      18
Extreme support plane      74 76
Face      18 62
Face, exposed      63 65
Face, isolated      79
Face, perfect      73
Face, proper      62
Face, strongly connected family of faces      152
Face-function      66
Facet      62 96
1 2 3 4
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