메뉴 건너뛰기




Volumn 231, Issue 2, 1999, Pages 568-587

Stability of inequalities in the dual Brunn-Minkowski theory

Author keywords

Geometric tomography; star body; convex body; isoperimetric inequality; Aleksandrov Fenchel inequality; Brunn Minkowski inequality; arithmetic geometric mean inequality; Clarkson's inequality; dual mixed volume; stability

Indexed keywords


EID: 0002383112     PISSN: 0022247X     EISSN: None     Source Type: Journal    
DOI: 10.1006/jmaa.1998.6254     Document Type: Article
Times cited : (11)

References (22)
  • 1
    • 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
  • 2
    • 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
  • 6
    • 0000722774 scopus 로고
    • Tomography of convex and star bodies
    • Gardner R. J., Volčič A. Tomography of convex and star bodies. Adv. Math. 108:1994;367-399.
    • (1994) Adv. Math. , vol.108 , pp. 367-399
    • Gardner, R.J.1    Volčič, A.2
  • 7
    • 0010716029 scopus 로고
    • Stability results for first order projection bodies
    • Goodey P. R., Groemer H. Stability results for first order projection bodies. Proc. Amer. Math. Soc. 109:1990;1103-1114.
    • (1990) Proc. Amer. Math. Soc. , vol.109 , pp. 1103-1114
    • Goodey, P.R.1    Groemer, H.2
  • 8
    • 0347841023 scopus 로고
    • On the Brunn-Minkowski theorem
    • Groemer H. On the Brunn-Minkowski theorem. Geom. Dedicata. 27:1988;357-371.
    • (1988) Geom. Dedicata , vol.27 , pp. 357-371
    • Groemer, H.1
  • 9
    • 0002264365 scopus 로고
    • On an inequality of Minkowski for mixed volumes
    • Groemer H. On an inequality of Minkowski for mixed volumes. Geom. Dedicata. 33:1990;117-122.
    • (1990) Geom. Dedicata , vol.33 , pp. 117-122
    • Groemer, H.1
  • 10
    • 0001082064 scopus 로고
    • Stability of geometric inequalities
    • P. M. Gruber, & J. M. Wills. Amsterdam: North-Holland
    • Groemer H. Stability of geometric inequalities. Gruber P. M., Wills J. M. Handbook of Convexity. 1993;125-150 North-Holland, Amsterdam.
    • (1993) Handbook of Convexity , pp. 125-150
    • Groemer, H.1
  • 13
    • 84968510078 scopus 로고
    • On the arithmetic and geometric means and on Hölder's inequality
    • Kober H. On the arithmetic and geometric means and on Hölder's inequality. Proc. Amer. Math. Soc. 9:1958;452-459.
    • (1958) Proc. Amer. Math. Soc. , vol.9 , pp. 452-459
    • Kober, H.1
  • 14
    • 84972548660 scopus 로고
    • Dual mixed volumes
    • Lutwak E. Dual mixed volumes. Pacific J. Math. 58:1975;531-538.
    • (1975) Pacific J. Math. , vol.58 , pp. 531-538
    • Lutwak, E.1
  • 17
    • 84975994710 scopus 로고
    • Stability in the Aleksandrov-Fenchel-Jessen theorem
    • Schneider R. Stability in the Aleksandrov-Fenchel-Jessen theorem. Mathematika. 36:1989;50-59.
    • (1989) Mathematika , vol.36 , pp. 50-59
    • Schneider, R.1
  • 18
    • 51249178332 scopus 로고
    • A stability estimate for the Aleksandrov-Fenchel inequality with an application to mean curvature
    • Schneider R. A stability estimate for the Aleksandrov-Fenchel inequality with an application to mean curvature. Manuscripta Math. 69:1990;291-300.
    • (1990) Manuscripta Math. , vol.69 , pp. 291-300
    • Schneider, R.1
  • 20
    • 0001367476 scopus 로고
    • pmetrics for compact, convex sets
    • pmetrics for compact, convex sets. J. Approx. Theory. 45:1985;280-287.
    • (1985) J. Approx. Theory , vol.45 , pp. 280-287
    • Vitale, R.A.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.