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Volumn 170, Issue 2, 2002, Pages 239-256

Valuations of polytopes containing the origin in their interiors

Author keywords

Hadwiger's characterization theorem; Valuations

Indexed keywords


EID: 0037174520     PISSN: 00018708     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0001-8708(02)92077-3     Document Type: Article
Times cited : (58)

References (22)
  • 1
    • 0003638666 scopus 로고
    • "Lectures on Functional Equations and their Applications"
    • Academic Press, New York
    • J. Aczel, "Lectures on Functional Equations and their Applications," Academic Press, New York, 1966.
    • (1966)
    • Aczel, J.1
  • 2
    • 0032222145 scopus 로고    scopus 로고
    • Continuous valuations on convex sets
    • S. Alesker, Continuous valuations on convex sets, Geom. Funct. Anal. 8 (1998), 402-409.
    • (1998) Geom. Funct. Anal , vol.8 , pp. 402-409
    • Alesker, S.1
  • 3
    • 0033416837 scopus 로고    scopus 로고
    • Continuous rotation invariant valuations on convex sets
    • S. Alesker, Continuous rotation invariant valuations on convex sets, Ann. of Math. (2) 149 (1999), 977-1005.
    • (1999) Ann. of Math , vol.149 , Issue.2 , pp. 977-1005
    • Alesker, S.1
  • 4
    • 0000287587 scopus 로고    scopus 로고
    • Description of continuous isometry covariant valuations on convex sets
    • S. Alesker, Description of continuous isometry covariant valuations on convex sets, Geom. Dedicata 74 (1999), 241-248.
    • (1999) Geom. Dedicata , vol.74 , pp. 241-248
    • Alesker, S.1
  • 5
    • 0034634093 scopus 로고    scopus 로고
    • On P. McMullen's conjecture on translation invariant valuations
    • S. Alesker, On P. McMullen's conjecture on translation invariant valuations, Adv. Math. 155 (2000), 239-263.
    • (2000) Adv. Math , vol.155 , pp. 239-263
    • Alesker, S.1
  • 6
    • 0035611289 scopus 로고    scopus 로고
    • Description of translation invariant valuations on convex sets with solution of P. McMullen's conjecture
    • S. Alesker, Description of translation invariant valuations on convex sets with solution of P. McMullen's conjecture, Geom. Funct. Anal. 11 (2001), 244-272.
    • (2001) Geom. Funct. Anal , vol.11 , pp. 244-272
    • Alesker, S.1
  • 7
    • 0010980856 scopus 로고
    • Additive Funktionale k-dimensionaler Eikörper, I
    • H. Hadwiger, Additive Funktionale k-dimensionaler Eikörper, I, Arch. Math. 3 (1952), 470-478.
    • (1952) Arch. Math , vol.3 , pp. 470-478
    • Hadwiger, H.1
  • 8
    • 0011009819 scopus 로고
    • Additive Funktionale k-dimensionaler Eikörper, II
    • H. Hadwiger, Additive Funktionale k-dimensionaler Eikörper, II, Arch. Math. 4 (1953), 374-379.
    • (1953) Arch. Math , vol.4 , pp. 374-379
    • Hadwiger, H.1
  • 9
    • 0003972254 scopus 로고
    • "Vorlesungen über Inhalt, Oberfläche und Isoperimetrie"
    • Springer, Berlin
    • H. Hadwiger, "Vorlesungen über Inhalt, Oberfläche und Isoperimetrie," Springer, Berlin, 1957.
    • (1957)
    • Hadwiger, H.1
  • 10
    • 84976126025 scopus 로고
    • A short proof of Hadwiger's characterization theorem
    • D. Klain, A short proof of Hadwiger's characterization theorem, Mathematika 42 (1995), 329-339.
    • (1995) Mathematika , vol.42 , pp. 329-339
    • Klain, D.1
  • 11
    • 0030585828 scopus 로고    scopus 로고
    • Star valuations and dual mixed volumes
    • D. Klain, Star valuations and dual mixed volumes, Adv. Math. 121 (1996), 80-101.
    • (1996) Adv. Math , vol.121 , pp. 80-101
    • Klain, D.1
  • 12
    • 0031568184 scopus 로고    scopus 로고
    • Invariant valuations on star-shaped sets
    • D. Klain, Invariant valuations on star-shaped sets, Adv. Math. 125 (1997), 95-113.
    • (1997) Adv. Math , vol.125 , pp. 95-113
    • Klain, D.1
  • 13
    • 22844456159 scopus 로고    scopus 로고
    • Even valuations on convex bodies
    • D. Klain, Even valuations on convex bodies, Trans. Amer. Math. Soc. 352 (2000), 71-93.
    • (2000) Trans. Amer. Math. Soc , vol.352 , pp. 71-93
    • Klain, D.1
  • 14
    • 0004119908 scopus 로고    scopus 로고
    • "Introduction to Geometric Probability"
    • Cambridge Univ. Press, Cambridge, UK
    • D. Klain and G. Rota, "Introduction to Geometric Probability," Cambridge Univ. Press, Cambridge, UK, 1997.
    • (1997)
    • Klain, D.1    Rota, G.2
  • 15
    • 0010981587 scopus 로고    scopus 로고
    • A characterization of affine length and asymptotic approximation of convex discs
    • M. Ludwig, A characterization of affine length and asymptotic approximation of convex discs, Abh. Math. Semin. Univ. Hamb. 69 (1999), 75-88.
    • (1999) Abh. Math. Semin. Univ. Hamb , vol.69 , pp. 75-88
    • Ludwig, M.1
  • 16
    • 0010981202 scopus 로고    scopus 로고
    • Upper semicontinuous valuations on the space of convex discs
    • M. Ludwig, Upper semicontinuous valuations on the space of convex discs, Geom. Dedicata 80 (2000), 263-279.
    • (2000) Geom. Dedicata , vol.80 , pp. 263-279
    • Ludwig, M.1
  • 17
    • 0000537779 scopus 로고    scopus 로고
    • A characterization of affine surface area
    • M. Ludwig and M. Reitzner, A characterization of affine surface area, Adv. Math. 147 (1999), 138-172.
    • (1999) Adv. Math , vol.147 , pp. 138-172
    • Ludwig, M.1    Reitzner, M.2
  • 18
    • 0030600832 scopus 로고    scopus 로고
    • The Brunn-Minkowski-Firey theory, II: Affine and geominimal surface areas
    • E. Lutwak, The Brunn-Minkowski-Firey theory, II: Affine and geominimal surface areas, Adv. Math. 118 (1996), 244-294.
    • (1996) Adv. Math , vol.118 , pp. 244-294
    • Lutwak, E.1
  • 19
    • 0001635748 scopus 로고
    • Continuous translation-invariant valuations on the space of compact convex sets
    • P. McMullen, Continuous translation-invariant valuations on the space of compact convex sets, Arch. Math. 55 (1980), 377-384.
    • (1980) Arch. Math , vol.55 , pp. 377-384
    • McMullen, P.1
  • 20
    • 0001968639 scopus 로고
    • Valuations and dissection
    • (P.M. Gruber and J. Wills, Eds.), North-Holland, Amsterdam
    • P. McMullen, Valuations and dissection, in "Handbook of Convex Geometry B" (P.M. Gruber and J. Wills, Eds.), pp. 933-990, North-Holland, Amsterdam, 1993.
    • (1993) "Handbook of Convex Geometry B" , pp. 933-990
    • McMullen, P.1
  • 21
    • 0002634852 scopus 로고
    • Valuations on convex bodies
    • (P.M. Gruber and J. Wills, Eds.), Birkhäuser, Basel
    • P. McMullen and R. Schneider, Valuations on convex bodies, in "Convexity and its Applications" (P.M. Gruber and J. Wills, Eds.), pp. 170-247, Birkhäuser, Basel, 1983.
    • (1983) "Convexity and Its Applications" , pp. 170-247
    • McMullen, P.1    Schneider, R.2
  • 22
    • 21344466360 scopus 로고    scopus 로고
    • Simple valuations on convex bodies
    • R. Schneider, Simple valuations on convex bodies, Mathematika 43 (1996), 32-39.
    • (1996) Mathematika , vol.43 , pp. 32-39
    • Schneider, R.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.