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Volumn 117, Issue , 2000, Pages 29-60

Extremal problems and isotropic positions of convex bodies

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EID: 0039334944     PISSN: 00212172     EISSN: 15658511     Source Type: Journal    
DOI: 10.1007/BF02773562     Document Type: Article
Times cited : (80)

References (32)
  • 1
    • 0011606837 scopus 로고
    • On the theory of mixed volumes of convex bodies, I, extension of certain concepts in the theory of convex bodies
    • A. D. Alexandrov, On the theory of mixed volumes of convex bodies, I, Extension of certain concepts in the theory of convex bodies (in Russian), Matematicheskii Sbornik N.S. 2 (1937), 947-972.
    • (1937) Matematicheskii Sbornik N.S. , vol.2 , pp. 947-972
    • Alexandrov, A.D.1
  • 2
    • 0040281259 scopus 로고
    • On the surface area functions of convex bodies
    • A. D. Alexandrov, On the surface area functions of convex bodies (in Russian), Matematicheskii Sbornik N.S. 6(48) (1939), 167-174.
    • (1939) Matematicheskii Sbornik N.S. , vol.6 , Issue.48 , pp. 167-174
    • Alexandrov, A.D.1
  • 3
    • 0001204968 scopus 로고
    • Volumes of sections of cubes and related problems
    • Springer-Verlag, Berlin
    • K. M. Ball, Volumes of sections of cubes and related problems, Lecture Notes in Mathematics 1376, Springer-Verlag, Berlin, 1989, pp. 251-260.
    • (1989) Lecture Notes in Mathematics , vol.1376 , pp. 251-260
    • Ball, K.M.1
  • 6
    • 0000662974 scopus 로고
    • Ellipsoids of maximal volume in convex bodies
    • K. M. Ball, Ellipsoids of maximal volume in convex bodies, Geometriae Dedicata 41 (1992), 241-250.
    • (1992) Geometriae Dedicata , vol.41 , pp. 241-250
    • Ball, K.M.1
  • 7
    • 0032350790 scopus 로고    scopus 로고
    • On a reverse form of the Brascamp-Lieb inequality
    • F. Barthe, On a reverse form of the Brascamp-Lieb inequality, Inventiones Mathematicae 134 (1998), 335-361.
    • (1998) Inventiones Mathematicae , vol.134 , pp. 335-361
    • Barthe, F.1
  • 8
    • 0040875521 scopus 로고
    • Integral representations of quermassintegrals and Bonnesen-style inequalities
    • J. Bokowski and E. Heil, Integral representations of quermassintegrals and Bonnesen-style inequalities, Archiv der Mathematik 47 (1986), 79-89.
    • (1986) Archiv der Mathematik , vol.47 , pp. 79-89
    • Bokowski, J.1    Heil, E.2
  • 10
    • 84968504856 scopus 로고
    • The determination of convex bodies from their mean radius of curvature functions
    • W. J. Firey, The determination of convex bodies from their mean radius of curvature functions, Mathematika 14 (1967), 1-13.
    • (1967) Mathematika , vol.14 , pp. 1-13
    • Firey, W.J.1
  • 13
    • 0040281255 scopus 로고    scopus 로고
    • Geometric applications of fourier series and spherical harmonics
    • Cambridge University Press, Cambridge
    • H. Groemer, Geometric Applications of Fourier Series and Spherical Harmonics, Encyclopedia of Mathematics and its Applications 61, Cambridge University Press, Cambridge, 1996.
    • (1996) Encyclopedia of Mathematics and Its Applications , vol.61
    • Groemer, H.1
  • 15
    • 0000727804 scopus 로고    scopus 로고
    • An isomorphic Dvoretzky's theorem for convex bodies
    • Y. Gordon, O. Guédon and M. Meyer, An isomorphic Dvoretzky's theorem for convex bodies, Studia Mathematica 127 (1998), 191-200.
    • (1998) Studia Mathematica , vol.127 , pp. 191-200
    • Gordon, Y.1    Guédon, O.2    Meyer, M.3
  • 16
    • 0002940114 scopus 로고
    • Extremum problems with inequalities as subsidiary conditions
    • Interscience, New York
    • F. John, Extremum problems with inequalities as subsidiary conditions, in Courant Anniversary Volume, Interscience, New York, 1948, pp. 187-204.
    • (1948) Courant Anniversary Volume , pp. 187-204
    • John, F.1
  • 17
    • 84972273330 scopus 로고
    • Ellipsoids defined by Banach ideal norms
    • D. R. Lewis, Ellipsoids defined by Banach ideal norms, Mathematika 26 (1979), 18-29.
    • (1979) Mathematika , vol.26 , pp. 18-29
    • Lewis, D.R.1
  • 18
    • 0013517079 scopus 로고
    • Random subspaces of proportional dimension of finite dimensional normed spaces: Approach through the isoperimetric inequality
    • Springer-Verlag, Berlin
    • V. D. Milman, Random subspaces of proportional dimension of finite dimensional normed spaces: Approach through the isoperimetric inequality, Lecture Notes in Mathematics 1166, Springer-Verlag, Berlin, 1985, pp. 106-115.
    • (1985) Lecture Notes in Mathematics , vol.1166 , pp. 106-115
    • Milman, V.D.1
  • 19
    • 0002090375 scopus 로고
    • Inégalité de Brunn-Minkowski inverse et applications à la théorie locale des espaces normés
    • V. D. Milman, Inégalité de Brunn-Minkowski inverse et applications à la théorie locale des espaces normés, Comptes Rendus de l'Académie des Sciences, Paris 302 (1986), 25-28.
    • (1986) Comptes Rendus de l'Académie des Sciences, Paris , vol.302 , pp. 25-28
    • Milman, V.D.1
  • 20
    • 0002904748 scopus 로고
    • Isotropic position and inertia ellipsoids and zonoids of the unit ball of a normed n-dimensional space
    • Springer-Verlag, Berlin
    • V. D. Milman and A. Pajor, Isotropic position and inertia ellipsoids and zonoids of the unit ball of a normed n-dimensional space, Lecture Notes in Mathematics 1376, Springer-Verlag, Berlin, 1989, pp. 64-104.
    • (1989) Lecture Notes in Mathematics , vol.1376 , pp. 64-104
    • Milman, V.D.1    Pajor, A.2
  • 22
    • 0003270948 scopus 로고
    • Asymptotic theory of finite dimensional normed spaces
    • Springer-Verlag, Berlin
    • V. D. Milman and G. Schechtman, Asymptotic Theory of Finite Dimensional Normed Spaces, Lecture Notes in Mathematics 1200, Springer-Verlag, Berlin, 1986.
    • (1986) Lecture Notes in Mathematics , vol.1200
    • Milman, V.D.1    Schechtman, G.2
  • 23
    • 0003054854 scopus 로고    scopus 로고
    • Global versus local asymptotic theories of finite-dimensional normed spaces
    • V. D. Milman and G. Schechtman, Global versus Local asymptotic theories of finite-dimensional normed spaces, Duke Mathematical Journal 90 (1997), 73-93.
    • (1997) Duke Mathematical Journal , vol.90 , pp. 73-93
    • Milman, V.D.1    Schechtman, G.2
  • 25
    • 0002049763 scopus 로고
    • Surface area of a convex body under affine transformations
    • C. M. Petty, Surface area of a convex body under affine transformations, Proceedings of the American Mathematical Society 12 (1961), 824-828.
    • (1961) Proceedings of the American Mathematical Society , vol.12 , pp. 824-828
    • Petty, C.M.1
  • 26
    • 0001266043 scopus 로고
    • Holomorphic semi-groups and the geometry of Banach spaces
    • G. Pisier, Holomorphic semi-groups and the geometry of Banach spaces, Annals of Mathematics 115 (1982), 375-392.
    • (1982) Annals of Mathematics , vol.115 , pp. 375-392
    • Pisier, G.1
  • 27
    • 0003254209 scopus 로고
    • The volume of convex bodies and Banach space geometry
    • Cambridge University Press
    • G. Pisier, The Volume of Convex Bodies and Banach Space Geometry, Cambridge Tracts in Mathematics 94, Cambridge University Press, 1989.
    • (1989) Cambridge Tracts in Mathematics , vol.94
    • Pisier, G.1
  • 29
    • 0001142604 scopus 로고
    • On the Hessian of a function and the curvatures of its graph
    • R. C. Reilly, On the Hessian of a function and the curvatures of its graph, The Michigan Mathematical Journal 20 (1973), 373-383.
    • (1973) The Michigan Mathematical Journal , vol.20 , pp. 373-383
    • Reilly, R.C.1
  • 31
    • 0003333144 scopus 로고
    • Convex bodies: The Brunn-Minkowski theory
    • Cambridge University Press, Cambridge
    • R. Schneider, Convex Bodies: The Brunn-Minkowski Theory, Encyclopedia of Mathematics and its Applications 44, Cambridge University Press, Cambridge, 1993.
    • (1993) Encyclopedia of Mathematics and Its Applications , vol.44
    • Schneider, R.1
  • 32
    • 0003227837 scopus 로고
    • Banach-Mazur distances and finite dimensional operator ideals
    • Pitman, London
    • N. Tomczak-Jaegermann, Banach-Mazur Distances and Finite Dimensional Operator Ideals, Pitman Monographs 38, Pitman, London, 1989.
    • (1989) Pitman Monographs , vol.38
    • Tomczak-Jaegermann, N.1


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