메뉴 건너뛰기




Volumn 328, Issue 1, 1999, Pages 29-34

An analytic solution to the Busemann-Petty problem

Author keywords

[No Author keywords available]

Indexed keywords


EID: 0032623055     PISSN: 07644442     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0764-4442(99)80007-X     Document Type: Article
Times cited : (8)

References (23)
  • 1
    • 0001642631 scopus 로고
    • Some remarks on the geometry of convex sets
    • Lindenstrauss J., Milman V.D. (Eds), Springer, Heidelberg
    • Ball K., Some remarks on the geometry of convex sets, In: Lindenstrauss J., Milman V.D. (Eds), Geometric Aspects of Functional Analysis: Lecture Notes in Mathematics 1317, Springer, Heidelberg, 1988, pp. 224-231.
    • (1988) Geometric Aspects of Functional Analysis: Lecture Notes in Mathematics , vol.1317 , pp. 224-231
    • Ball, K.1
  • 2
    • 0003373303 scopus 로고
    • On the Busemann-Petty problem for perturbations of the ball
    • Bourgain J., On the Busemann-Petty problem for perturbations of the ball, Geom. Funct. Anal. 1 (1991) 1-13.
    • (1991) Geom. Funct. Anal. , vol.1 , pp. 1-13
    • Bourgain, J.1
  • 3
    • 0001775494 scopus 로고
    • Problems on convex bodies
    • Busemann H., Petty C.M., Problems on convex bodies, Math. Scand. 4 (1956) 88-94.
    • (1956) Math. Scand. , vol.4 , pp. 88-94
    • Busemann, H.1    Petty, C.M.2
  • 4
    • 0001869895 scopus 로고
    • Intersection bodies and the Busemann-Petty problem
    • Gardner R.J., Intersection bodies and the Busemann-Petty problem, Trans. Amer. Math. Soc. 342 (1994) 435-445.
    • (1994) Trans. Amer. Math. Soc. , vol.342 , pp. 435-445
    • Gardner, R.J.1
  • 5
    • 0001869896 scopus 로고
    • A positive answer to the Busemann-Petty problem in three dimensions
    • Gardner R.J., A positive answer to the Busemann-Petty problem in three dimensions, Ann. Math. 140 (1994) 435-447.
    • (1994) Ann. Math. , vol.140 , pp. 435-447
    • Gardner, R.J.1
  • 7
    • 0040067077 scopus 로고    scopus 로고
    • An analytic solution to the Busemann-Petty problem on sections of convex bodies
    • to appear
    • Gardner R.J., Koldobsky A., Schlumprecht Th., An analytic solution to the Busemann-Petty problem on sections of convex bodies Ann. Math. (to appear).
    • Ann. Math.
    • Gardner, R.J.1    Koldobsky, A.2    Schlumprecht, Th.3
  • 10
    • 84975992354 scopus 로고
    • A note on a problem of H. Busemann and C. M. Petty concerning sections of symmetric convex bodies
    • Giannopoulos A., A note on a problem of H. Busemann and C. M. Petty concerning sections of symmetric convex bodies, Mathematika 37 (1990) 239-244.
    • (1990) Mathematika , vol.37 , pp. 239-244
    • Giannopoulos, A.1
  • 11
    • 0003180011 scopus 로고
    • Schoenberg's problem on positive definite functions
    • Koldobsky A., Schoenberg's problem on positive definite functions, Algebra and Analysis 3 (1991) 78-85. English translation in St. Petersburg Math. J. 3 (1992) 563-570.
    • (1991) Algebra and Analysis , vol.3 , pp. 78-85
    • Koldobsky, A.1
  • 12
    • 0003180013 scopus 로고
    • Koldobsky A., Schoenberg's problem on positive definite functions, Algebra and Analysis 3 (1991) 78-85. English translation in St. Petersburg Math. J. 3 (1992) 563-570.
    • (1992) St. Petersburg Math. J. , vol.3 , pp. 563-570
  • 13
    • 0032430369 scopus 로고    scopus 로고
    • An application of the Fourier transform to sections of star bodies
    • Koldobsky A., An application of the Fourier transform to sections of star bodies, Israel J. Math. 106 (1998) 157-164.
    • (1998) Israel J. Math. , vol.106 , pp. 157-164
    • Koldobsky, A.1
  • 14
    • 0000918923 scopus 로고    scopus 로고
    • Intersection bodies, positive definite distributions and the Busemann-Petty problem
    • Koldobsky A., Intersection bodies, positive definite distributions and the Busemann-Petty problem, Amer. J. Math. 120 (1998) 827-840.
    • (1998) Amer. J. Math. , vol.120 , pp. 827-840
    • Koldobsky, A.1
  • 16
    • 0031537215 scopus 로고    scopus 로고
    • Intersection bodies and the Busemann-Petty problem
    • série I
    • Koldobsky A., Intersection bodies and the Busemann-Petty problem, C.R. Acad. Sci. Paris 325 série I (1997) 1181-1186.
    • (1997) C.R. Acad. Sci. Paris , vol.325 , pp. 1181-1186
    • Koldobsky, A.1
  • 17
    • 84971946870 scopus 로고
    • The existence of a centrally symmetric convex body with central sections that are unexpectedly small
    • Larman D.G., Rogers C.A., The existence of a centrally symmetric convex body with central sections that are unexpectedly small, Mathematika 22 (1975) 164-175.
    • (1975) Mathematika , vol.22 , pp. 164-175
    • Larman, D.G.1    Rogers, C.A.2
  • 18
    • 0000830163 scopus 로고
    • Intersection bodies and dual mixed volumes
    • Lutwak E., Intersection bodies and dual mixed volumes, Advances in Math. 71 (1988) 232-261.
    • (1988) Advances in Math. , vol.71 , pp. 232-261
    • Lutwak, E.1
  • 21
    • 0000235581 scopus 로고
    • Centered bodies and dual mixed volumes
    • Zhang G., Centered bodies and dual mixed volumes, Trans. Amer. Math. Soc. 345 (1994) 777-801.
    • (1994) Trans. Amer. Math. Soc. , vol.345 , pp. 777-801
    • Zhang, G.1
  • 23
    • 0010984856 scopus 로고    scopus 로고
    • A positive answer to the Busemann-Petty problem in four dimensions
    • to appear
    • Zhang G., A positive answer to the Busemann-Petty problem in four dimensions, Ann. Math. (to appear).
    • Ann. Math.
    • Zhang, G.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.