메뉴 건너뛰기




Volumn 29, Issue , 1998, Pages 215-265

Measures in convex geometry

Author keywords

[No Author keywords available]

Indexed keywords


EID: 33750529203     PISSN: 00494704     EISSN: 24648728     Source Type: Journal    
DOI: None     Document Type: Article
Times cited : (6)

References (51)
  • 1
    • 0002967985 scopus 로고
    • On the structure of singular sets of convex functions
    • G. ALBERTI, On the structure of singular sets of convex functions, Calc. Var. 2 (1994), 17-27
    • (1994) Calc. Var , vol.2 , pp. 17-27
    • Alberti, G.1
  • 2
  • 3
    • 0011606837 scopus 로고
    • Zur Theorie der gemischten Volumina von kon-vexen Korpern. I. Verallgemeinerung einiger Begriffe der Theorie der konvexen Korper (in Rssian)
    • A. D. ALEKSANDROV, Zur Theorie der gemischten Volumina von kon-vexen Korpern. I. Verallgemeinerung einiger Begriffe der Theorie der konvexen Korper (in Rssian), Mat. Sb. N. S. 2 (1937), 947-972
    • (1937) Mat. Sb. N. S , vol.2 , pp. 947-972
    • Aleksandrov, A.D.1
  • 5
    • 0000864732 scopus 로고
    • Zur Theorie der gemischten Volumina von konvexen Korpern. v III. Die Erweiterung zweier Lehrsatze Minkowskis iiber die konvexen Polyeder auf beliebige konvexe Flachen (in Rssian)
    • A. D. ALEKSANDROV, Zur Theorie der gemischten Volumina von konvexen Korpern. v III. Die Erweiterung zweier Lehrsatze Minkowskis iiber die konvexen Polyeder auf beliebige konvexe Flachen (in Rssian), Mat. Sb. N. S. 3 (1938), 27-46
    • (1938) Mat. Sb. N. S , vol.3 , pp. 27-46
    • Aleksandrov, A.D.1
  • 6
    • 0040281259 scopus 로고
    • Uber die Oberflachenfunktion eines konvexen Korpers (in Russian)
    • A. D. ALEKSANDROV, Uber die Oberflachenfunktion eines konvexen Korpers (in Russian), Mat. Sb. N. S. 6 (1939), 167-174
    • (1939) Mat. Sb. N. S , vol.6 , pp. 167-174
    • Aleksandrov, A.D.1
  • 7
    • 0039229304 scopus 로고
    • Smothness of the convex surface of bounded Gaussian curvature, . R (Doklady)
    • A. D. ALEKSANDROV, Smothness of the convex surface of bounded Gaussian curvature, . R (Doklady) Acad. Sci. URSS 36 1942) 195-199
    • (1942) Acad. Sci. URSS , vol.36 , pp. 195-199
    • Aleksandrov, A.D.1
  • 8
    • 84972535466 scopus 로고
    • Convex functions and upper semicontinuous collections
    • R. D. ANDERSON AND V. L. KLEE, Convex functions and upper semicontinuous collections, Duke Math. J. 19 (1952), 349-357
    • (1952) Duke Math. J , vol.19 , pp. 349-357
    • Anderson, R.D.1    Klee, V.L.2
  • 10
    • 0043040852 scopus 로고    scopus 로고
    • Minimal and reduced pairs convex bodies
    • C. BAUER, Minimal and reduced pairs convex bodies, Geom. Dedi cata 62 (1996), 179-192
    • (1996) Geom. Dedi cata , vol.62 , pp. 179-192
    • Bauer, C.1
  • 13
    • 0000360790 scopus 로고
    • A class of convex bodies
    • E. D. BOLKER, A class of convex bodies, Trans. mer ath. Soc. 145 (1969), 323-346
    • (1969) Trans. mer ath. Soc , vol.145 , pp. 323-346
    • Bolker, E.D.1
  • 14
    • 0005422146 scopus 로고    scopus 로고
    • On smoothness and singularities of convex hypersurfaces
    • Yu. BURAGO AND B. KALININ, On smoothness and singularities of convex hypersurfaces, S. Petersburg Math. J. 8 (1997), 399-411
    • (1997) S. Petersburg Math. J , vol.8 , pp. 399-411
    • Burago, Y.1    Kalinin, B.2
  • 16
    • 0011867297 scopus 로고
    • Integral formulas for hypersurfaces i euclidean space and their applications uniqueness theorems
    • S. S. CHERN, Integral formulas for hypersurfaces i euclidean space and their applications uniqueness theorems J. ath ech. 8 (1959), 947-955
    • (1959) J. ath ech , vol.8 , pp. 947-955
    • Chern, S.S.1
  • 17
    • 84972015971 scopus 로고
    • The directions of the line segments and of the r-dimensional balls on the boundary of a convex body in Euclidean space
    • G. EWALD, D. G. LARMAN, AND C. A. ROGERS, The directions of the line segments and of the r-dimensional balls on the boundary of a convex body in Euclidean space, Mathematika 17 (1970), 1-20
    • (1970) Mathematika , vol.17 , pp. 1-20
    • Ewald, G.1    Larman, D.G.2    Rogers, C.A.3
  • 18
    • 84968469617 scopus 로고    scopus 로고
    • Curvature measures
    • H. FEDERER, Curvature measures, Trans. mer ath. Soc. 93 959), 418-491
    • Trans. mer ath. Soc , vol.93 , Issue.959 , pp. 418-491
    • Federer, H.1
  • 19
    • 0001825289 scopus 로고
    • Mengenfunktionen und konvexe Korper. anske Vid
    • W. FENCHEL AND B. JESSEN, Mengenfunktionen und konvexe Korper, anske Vid. Selskab at.fys. edd. 16 1938), no. 3, 1-31
    • (1938) Selskab at.fys. edd , vol.16 , Issue.3 , pp. 1-31
    • Fenchel, W.1    Jessen, B.2
  • 22
    • 0002517837 scopus 로고
    • Zonoids and generalizations
    • (Amsterdam) (P. M ruber and J.M. Wll eds.) Elsevier
    • P. GOODEY AND W. WEIL, Zonoids and generalizations, Handbook of Convex Geometry (Amsterdam) (P. M ruber and J.M. Wll eds.), vol. B, Elsevier, 1993, pp. 1297-1326
    • (1993) Handbook of Convex Geometry , vol.B , pp. 1297-1326
    • Goodey, P.1    Weil, W.2
  • 23
    • 0040415345 scopus 로고
    • Translationsinvariante, additive und stetige Eibereich-funktionale
    • H. HADWIGER, Translationsinvariante, additive und stetige Eibereich-funktionale, Publ. Math. Debrecen 2 (1951), 81-84
    • (1951) Publ. Math. Debrecen , vol.2 , pp. 81-84
    • Hadwiger, H.1
  • 24
    • 0001466381 scopus 로고
    • On the mean number of normals trough a point in the interior of a convex body
    • D. HUG, On the mean number of normals trough a point in the interior of a convex body, Geom. Dedicata 55 (1995), 319-340
    • (1995) Geom. Dedicata , vol.55 , pp. 319-340
    • Hug, D.1
  • 25
    • 85046758191 scopus 로고
    • Minkowskigleichungen und Charakterisierungen metrischer Ball in aumformen, Dissertation Universitat Dortmund
    • P. KOHLMANN, Kriimmungsmafle, Minkowskigleichungen und Charakterisierungen metrischer Ball in aumformen, Dissertation Universitat Dortmund, 1988
    • (1988) Kriimmungsmafle
    • Kohlmann, P.1
  • 26
    • 0000644398 scopus 로고
    • Curvature measures and Steiner formulae i space forms
    • P. KOHLMANN, Curvature measures and Steiner formulae i space forms, Geom. Dedicata 40 (1991), 191-211
    • (1991) Geom. Dedicata , vol.40 , pp. 191-211
    • Kohlmann, P.1
  • 27
    • 0000060650 scopus 로고
    • Minkowski integral formulas for compact convex bodies in standard space forms
    • P. KOHLMANN, Minkowski integral formulas for compact convex bodies in standard space forms, Math. Nachr 166 (1994), 217-228
    • (1994) Math. Nachr , vol.166 , pp. 217-228
    • Kohlmann, P.1
  • 28
    • 0040413681 scopus 로고
    • Compact convex bodies with one curvature measure near the surface measure
    • P. KOHLMANN, Compact convex bodies with one curvature measure near the surface measure, J. reine angew Math. 458 (1995), 201-217
    • (1995) J. reine angew Math , vol.458 , pp. 201-217
    • Kohlmann, P.1
  • 29
    • 0039821204 scopus 로고    scopus 로고
    • Splitting and pinching for convex sets
    • P. KOHLMANN, Splitting and pinching for convex sets, Geometria Dedicata 60 (1996), 125-143
    • (1996) Geometria Dedicata , vol.60 , pp. 125-143
    • Kohlmann, P.1
  • 30
    • 0032222414 scopus 로고    scopus 로고
    • Characterization of metric balls in standard space forms via curvature measures
    • P. KOHLMANN, Characterization of metric balls in standard space forms via curvature measures, Math. Z. 227 (1998), 729-746
    • (1998) Math. Z , vol.227 , pp. 729-746
    • Kohlmann, P.1
  • 31
    • 79955165226 scopus 로고
    • Mesures sur le cercle et convexes du plan
    • G. LETAC, Mesures sur le cercle et convexes du plan, Ann. Sci. Univ. Clermont-Ferrand II 1 (1983), 35-65
    • (1983) Ann. Sci. Univ. Clermont-Ferrand II , vol.1 , pp. 35-65
    • Letac, G.1
  • 32
    • 0003281219 scopus 로고
    • Distribution of Zeros of Entire Functions
    • Providence, RI
    • B. J A. LEVIN, Distribution of Zeros of Entire Functions, AM Transl Math Monographs, vol. 5, Providence, RI 1964
    • (1964) AM Transl Math Monographs , vol.5
    • Levin, B.J.A.1
  • 34
    • 0002534146 scopus 로고
    • Allgemeine Lehrsatze iiber die konvexen Polyeder Nachr
    • Gesammele Abhand-lungen, (Teubner, Leipzig, 1911), pp 103-121
    • H. MINKOWSKI, Allgemeine Lehrsatze iiber die konvexen Polyeder Nachr. Ges. Wiss. Gottingen (1897), 198-219, Gesammele Abhand-lungen, Vol. II (Teubner, Leipzig, 1911), pp 103-121
    • (1897) Ges. Wiss. Gottingen , vol.2 , pp. 198-219
    • Minkowski, H.1
  • 36
    • 33845780711 scopus 로고
    • Bewegungsdquivariante, additive und stetige Trans-formationen konvexer Bereiche
    • R. SCHNEIDER, Bewegungsdquivariante, additive und stetige Trans-formationen konvexer Bereiche, Arch. Math. 25 (1974), 303-312
    • (1974) Arch. Math , vol.25 , pp. 303-312
    • Schneider, R.1
  • 37
    • 0001084115 scopus 로고
    • Kinematische Beriihrmafle und Integralrelationen fur Oberflachenmafie
    • R. SCHNEIDER, Kinematische Beriihrmafle und Integralrelationen fur Oberflachenmafie, Math. Ann. 218 1975), 253-267
    • (1975) Math. Ann , vol.218 , pp. 253-267
    • Schneider, R.1
  • 38
    • 0000868571 scopus 로고
    • Curvature measures of convex bodies
    • R. SCHNEIDER, Curvature measures of convex bodies, Ann at. Pura Appl. 116 1978), 101-134
    • (1978) Ann at. Pura Appl , vol.116 , pp. 101-134
    • Schneider, R.1
  • 39
    • 84971937652 scopus 로고
    • Kinematic measures for sets of colliding convex bodies
    • R. SCHNEIDER, Kinematic measures for sets of colliding convex bodies, Mathematika 25 (1978), 1-12
    • (1978) Mathematika , vol.25 , pp. 1-12
    • Schneider, R.1
  • 40
    • 51249182447 scopus 로고
    • Bestimmung konvexer Korper durch Krummungs-mafie
    • R. SCHNEIDER, Bestimmung konvexer Korper durch Krummungs-mafie, Comment. Math Helvet. 54 (1979), 4-60
    • (1979) Comment. Math Helvet , vol.54 , pp. 4-60
    • Schneider, R.1
  • 41
    • 0001153305 scopus 로고
    • Random hyperplanes meeting a convex body
    • R. SCHNEIDER, Random hyperplanes meeting a convex body, Wahr-scheinlichkeitsth. verw. Geb. 61 1982), 379-387
    • (1982) Wahr-scheinlichkeitsth. verw. Geb , vol.61 , pp. 379-387
    • Schneider, R.1
  • 42
    • 0003333144 scopus 로고
    • Convex Bodies: the Brunn-Minkowski Theory
    • Cambridge University Press Cambridge
    • R. SCHNEIDER, Convex Bodies: the Brunn-Minkowski Theory, Encyclopedia ath ppl vol 44, Cambridge University Press Cambridge, 1993
    • (1993) Encyclopedia ath ppl , vol.44
    • Schneider, R.1
  • 43
    • 0001358583 scopus 로고
    • Convex surfaces, curvature and surface area mea sures
    • (P. M Gruber and J.M. Will eds.) Elsevier, Amsterdam
    • R. SCHNEIDER, Convex surfaces, curvature and surface area mea sures, Handbook of Convex Geometry (P. M Gruber and J.M. Will eds.), vol. A, Elsevier, Amsterdam, 1993, pp. 273-299
    • (1993) Handbook of Convex Geometry , vol.A , pp. 273-299
    • Schneider, R.1
  • 46
    • 0002675053 scopus 로고
    • Integral geometry
    • (P. M. ruber and J.M. Wills eds.), vol Elsevier, Amsterdam
    • R. SCHNEIDER AND J. A. WIEACKER, Integral geometry, Handbook of Convex Geometry (P. M. ruber and J.M. Wills eds.), vol Elsevier, Amsterdam, 1993, pp 1349-1390
    • (1993) Handbook of Convex Geometry , pp. 1349-1390
    • Schneider, R.1    Wieacker, J.A.2
  • 47
    • 84972017656 scopus 로고
    • Minimal pairs o convex bodies in o dimensions
    • S. SCHOLTES, Minimal pairs o convex bodies in o dimensions, Mathematika 39 (1992), 267-273
    • (1992) Mathematika , vol.39 , pp. 267-273
    • Scholtes, S.1
  • 48
    • 0001014026 scopus 로고
    • Extremum properties of the intersection densities of stationary Poisson hyperplane processes
    • C. THOMAS, Extremum properties of the intersection densities of stationary Poisson hyperplane processes, Math. Operationsforsch. u Statist., Ser. Statist. 15 (1984), 443-449
    • (1984) Math. Operationsforsch. u Statist., Ser. Statist , vol.15 , pp. 443-449
    • Thomas, C.1
  • 49
    • 0002326139 scopus 로고
    • Stochastic geometry
    • (P. M. ruber and J.M. Wills eds.), vol sevier, Amsterdam
    • W. WEIL AND J. A. WIEACKER, Stochastic geometry, Handbook of Convex Geometry (P. M. ruber and J.M. Wills eds.), vol sevier, Amsterdam, 1993, pp. 1391-1438
    • (1993) Handbook of Convex Geometry , pp. 1391-1438
    • Weil, W.1    Wieacker, J.A.2
  • 50
    • 0000182794 scopus 로고
    • Integral and current representation of Federer' curvature easures
    • M. ZAHLE, Integral and current representation of Federer' curvature easures, Arch. Math. 46 (1986), 557-567
    • (1986) Arch. Math , vol.46 , pp. 557-567
    • Zahle, M.1
  • 51
    • 0000884525 scopus 로고
    • On the differentiation of convex functions in finite and infnite dimensional spaces
    • L. ZAJICEK, On the differentiation of convex functions in finite and infnite dimensional spaces, zech ath. J. 29 1979), 340-348
    • (1979) Zech ath. J , vol.29 , pp. 340-348
    • Zajicek, L.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.