메뉴 건너뛰기




Volumn 70, Issue 3, 1998, Pages 283-303

The Cross-Section Body, Plane Sections of Convex Bodies and Approximation of Convex Bodies, II

Author keywords

Approximation; Cross section body; Ellipsoids; Projections; Random polytopes; Sections

Indexed keywords


EID: 0039736383     PISSN: 00465755     EISSN: None     Source Type: Journal    
DOI: 10.1023/a:1004955802773     Document Type: Article
Times cited : (7)

References (30)
  • 1
    • 84972578861 scopus 로고
    • Content of the frustum of a simplex
    • MR 52#15232
    • Ali, M. M.: Content of the frustum of a simplex, Pacific J. Math. 48 (1973), 313-322, MR 52#15232.
    • (1973) Pacific J. Math. , vol.48 , pp. 313-322
    • Ali, M.M.1
  • 2
    • 0000683778 scopus 로고
    • Random polytopes in a convex polytope, independence of shape and concentration of vertices
    • MR 95g:52005
    • Bárány, I. and Buchta, Ch.: Random polytopes in a convex polytope, independence of shape and concentration of vertices, Math. Ann. 297 (1993), 467-497, MR 95g:52005.
    • (1993) Math. Ann. , vol.297 , pp. 467-497
    • Bárány, I.1    Buchta, Ch.2
  • 4
    • 0037908044 scopus 로고
    • On a Geometric Inequality, Geom. Aspects of Funct. Anal. (1986/87)
    • Springer, Berlin, New York, MR 89h:46012
    • Bourgain, J., Meyer, M., Milman, V. and Pajor, A.: On a Geometric Inequality, Geom. Aspects of Funct. Anal. (1986/87), Lecture Notes in Math. 1317, Springer, Berlin, New York, 1988, pp. 217-282 MR 89h:46012.
    • (1988) Lecture Notes in Math. 1317 , pp. 217-282
    • Bourgain, J.1    Meyer, M.2    Milman, V.3    Pajor, A.4
  • 5
    • 0002195406 scopus 로고
    • A theorem on convex bodies of the Brunn-Minkowski type
    • MR 10-395
    • Busemann, H.: A theorem on convex bodies of the Brunn-Minkowski type, Proc. Nat. Acad. Sci. USA 35 (1949), 27-31, MR 10-395.
    • (1949) Proc. Nat. Acad. Sci. USA , vol.35 , pp. 27-31
    • Busemann, H.1
  • 6
    • 84972496776 scopus 로고
    • Volume in terms of concurrent cross-sections
    • MR 14-1115
    • Busemann, H.: Volume in terms of concurrent cross-sections, Pacific J. Math. 3 (1953), 1-12, MR 14-1115.
    • (1953) Pacific J. Math. , vol.3 , pp. 1-12
    • Busemann, H.1
  • 7
    • 0003294426 scopus 로고
    • An Introduction to the Geometry of Numbers
    • Springer, Berlin, Göttingen, Heidelberg MR 28#1175
    • Cassels, J. W. S.: An Introduction to the Geometry of Numbers, Grundlehren Math. Wiss. 99, Springer, Berlin, Göttingen, Heidelberg 1959, MR 28#1175.
    • (1959) Grundlehren Math. Wiss. 99
    • Cassels, J.W.S.1
  • 8
    • 0042343178 scopus 로고
    • Volumes of a random polytope in a convex set, DIMACS Series in Discr. Math, and Theor. Comp. Sci. 4
    • 1991, Amer. Math. Soc., Providence, R.I., MR 92m:52008
    • Dalla, L. and Larman, D. G.: Volumes of a random polytope in a convex set, DIMACS Series in Discr. Math, and Theor. Comp. Sci. 4, 1991, Applied Geom. and Discr. Math., The Victor Klee Festschrift, Amer. Math. Soc., Providence, R.I., 1991, pp. 175-180, MR 92m:52008.
    • (1991) Applied Geom. and Discr. Math., the Victor Klee Festschrift , pp. 175-180
    • Dalla, L.1    Larman, D.G.2
  • 9
    • 0042844055 scopus 로고
    • Remarks on finite rank projections
    • MR 50#947
    • Davis, W. J.: Remarks on finite rank projections, J. Appr. Th. 9 (1973), 205-211, MR 50#947.
    • (1973) J. Appr. Th. , vol.9 , pp. 205-211
    • Davis, W.J.1
  • 10
    • 85045586558 scopus 로고    scopus 로고
    • Sections of convex bodies through their centroids
    • to appear
    • Fradelizi, M.: Sections of convex bodies through their centroids, Arch. Math., to appear.
    • Arch. Math.
    • Fradelizi, M.1
  • 11
    • 0009159757 scopus 로고
    • Der zentralsymmetrische Kern und die zentralsymmetrische Hülle von konvexen Körpern
    • MR 12-526
    • Fary, I. and Rédei, L.: Der zentralsymmetrische Kern und die zentralsymmetrische Hülle von konvexen Körpern, Math. Ann. 122 (1950), 205-220, MR 12-526.
    • (1950) Math. Ann. , vol.122 , pp. 205-220
    • Fary, I.1    Rédei, L.2
  • 12
    • 0004182159 scopus 로고
    • Cambridge University Press, Cambridge, MR 96j:52006
    • Gardner, R. J. Geometric Tomography, Cambridge University Press, Cambridge, 1995, MR 96j:52006.
    • (1995) Geometric Tomography
    • Gardner, R.J.1
  • 13
    • 84971985346 scopus 로고
    • On the mean value of the area of a random polygon in a plane convex body
    • MR 93m:52004
    • Giannopoulos, A. A. : On the mean value of the area of a random polygon in a plane convex body, Mathematika 39 (1992), 279-290. MR 93m:52004.
    • (1992) Mathematika , vol.39 , pp. 279-290
    • Giannopoulos, A.A.1
  • 14
    • 0041842010 scopus 로고
    • Zusammenhängende Lagerungen konvexer Köorper
    • MR 33#7935
    • Groemer, H.: Zusammenhängende Lagerungen konvexer Köorper, Math. Z. 94 (1966), 66-78, MR 33#7935.
    • (1966) Math. Z. , vol.94 , pp. 66-78
    • Groemer, H.1
  • 15
    • 84972556177 scopus 로고
    • On some mean values associated with a randomly selected simplex in a convex set
    • MR 47#5916
    • Groemer, H.: On some mean values associated with a randomly selected simplex in a convex set, Pacific J. Math. 45 (1973), 525-533, MR 47#5916.
    • (1973) Pacific J. Math. , vol.45 , pp. 525-533
    • Groemer, H.1
  • 16
    • 0013465628 scopus 로고
    • On the mean value of the volume of a random polytope in a convex set
    • (Basel) MR 49#6036
    • Groemer, H.: On the mean value of the volume of a random polytope in a convex set, Arch. Math. (Basel) 25 (1974), 86-90, MR 49#6036.
    • (1974) Arch. Math. , vol.25 , pp. 86-90
    • Groemer, H.1
  • 17
    • 0037608167 scopus 로고
    • On the average size of polytopes in a convex set
    • MR 84d:52013
    • Groemer, H.: On the average size of polytopes in a convex set, Geom. Dedicata 13 (1982), 47-62, MR 84d:52013.
    • (1982) Geom. Dedicata , vol.13 , pp. 47-62
    • Groemer, H.1
  • 18
    • 0002940114 scopus 로고
    • Extremum problems with inequalities as subsidiary conditions
    • Interscience, New York, MR 10-719
    • John, F.: Extremum problems with inequalities as subsidiary conditions. Studies and Essays, presented to R. Courant. Interscience, New York, 1948, pp, 187-204, MR 10-719.
    • (1948) Studies and Essays, Presented to R. Courant , pp. 187-204
    • John, F.1
  • 19
    • 0041341340 scopus 로고
    • Finite dimensional projection constants
    • MR 84k:46014
    • König, H., Lewis, D. R. and Lin, P. K.: Finite dimensional projection constants, Studia Math. 75 (1983), 341-358, MR 84k:46014.
    • (1983) Studia Math. , vol.75 , pp. 341-358
    • König, H.1    Lewis, D.R.2    Lin, P.K.3
  • 20
    • 0000275803 scopus 로고
    • Norms of minimal projections
    • MR 94m:46024
    • König, H., Tomczak-Jaegermann, N.: Norms of minimal projections, J. Funct. Anal. 119 (1994), 253-280, MR 94m:46024.
    • (1994) J. Funct. Anal. , vol.119 , pp. 253-280
    • König, H.1    Tomczak-Jaegermann, N.2
  • 21
    • 0039667580 scopus 로고
    • On some ellipsoid formulas of Busemann, Furstenberg and Tzkoni, Guggenheimer, and Petty
    • MR 92k:52014
    • Lutwak, E.: On some ellipsoid formulas of Busemann, Furstenberg and Tzkoni, Guggenheimer, and Petty, J. Math. Anal. Appl. 159 (1991), 18-26, MR 92k:52014.
    • (1991) J. Math. Anal. Appl. , vol.159 , pp. 18-26
    • Lutwak, E.1
  • 22
    • 0001946764 scopus 로고
    • Selected affine isoperimetric inequalities
    • P. M. Gruber and J. M. Wills (eds), North-Holland, Amsterdam, Oxford, New York, MR94h:52014
    • Lutwak, E.: Selected affine isoperimetric inequalities. In: P. M. Gruber and J. M. Wills (eds), Handbook of Convex Geometry, North-Holland, Amsterdam, Oxford, New York, 1993, pp. 151-176, MR94h:52014.
    • (1993) Handbook of Convex Geometry , pp. 151-176
    • Lutwak, E.1
  • 23
    • 0001243678 scopus 로고
    • An extremal property of the hypersphere
    • MR 12-526
    • Macbeath, A. M.: An extremal property of the hypersphere. Proc. Comb. Philos. Soc. 47 (1951), 245-247, MR 12-526.
    • (1951) Proc. Comb. Philos. Soc. , vol.47 , pp. 245-247
    • Macbeath, A.M.1
  • 24
    • 0040773824 scopus 로고
    • Five-neighbour packing of convex plates
    • Intuitive Geometry (Siófok, 1985), North-Holland, Amsterdam, New York, MR 88k:52019
    • Makai, Jr., E.: Five-neighbour packing of convex plates. Intuitive Geometry (Siófok, 1985), Colloq. Math. Soc. J. Bolyai 48, North-Holland, Amsterdam, New York, 1987, MR 88k:52019.
    • (1987) Colloq. Math. Soc. J. Bolyai , vol.48
    • Makai E., Jr.1
  • 25
    • 0000943921 scopus 로고    scopus 로고
    • The cross-section body, plane sections of convex bodies and approximation of convex bodies
    • MR 97m: 52013
    • Makai, Jr., E., and Martini, H.: The cross-section body, plane sections of convex bodies and approximation of convex bodies, I. Geom. Dedicata 63 (1996), 267-296, MR 97m: 52013.
    • (1996) I. Geom. Dedicata , vol.63 , pp. 267-296
    • Makai E., Jr.1    Martini, H.2
  • 27
    • 0002904748 scopus 로고
    • Isotropic position and inertia ellipsoids and zonoids of the unit ball of a normed n-dimensional space
    • Geometric Aspects of Functional Analysis, Israel Seminar (GAFA), 1987-88, Springer, Berlin, Heidelberg, MR 90g:52003
    • Milman, V. D., and Pajor, A. : Isotropic position and inertia ellipsoids and zonoids of the unit ball of a normed n-dimensional space, Geometric Aspects of Functional Analysis, Israel Seminar (GAFA), 1987-88, Lecture Notes in Math. 1376, Springer, Berlin, Heidelberg, 1989, pp. 64-104, MR 90g:52003.
    • (1989) Lecture Notes in Math. 1376 , pp. 64-104
    • Milman, V.D.1    Pajor, A.2
  • 28
    • 0041528313 scopus 로고
    • Plane sections of simplices
    • MR 47#7598
    • Philip, J.: Plane sections of simplices, Math. Prog. 3 (1972), 312-325, MR 47#7598.
    • (1972) Math. Prog. , vol.3 , pp. 312-325
    • Philip, J.1
  • 30
    • 0041528289 scopus 로고
    • A simplex with a large cross-section
    • MR 37#2095
    • Walkup, D. W.: A simplex with a large cross-section. Amer. Math. Monthly 75 (1968), 34-36, MR 37#2095.
    • (1968) Amer. Math. Monthly , vol.75 , pp. 34-36
    • Walkup, D.W.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.