메뉴 건너뛰기




Volumn 10, Issue 6, 1998, Pages 699-728

Generalized curvature measures and singularities of sets with positive reach

Author keywords

[No Author keywords available]

Indexed keywords


EID: 0032221844     PISSN: 09337741     EISSN: None     Source Type: Journal    
DOI: 10.1515/form.10.6.699     Document Type: Article
Times cited : (19)

References (28)
  • 1
    • 0002967985 scopus 로고
    • On the structure of singular sets of convex functions
    • Alberti, G.: 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
    • 51249167160 scopus 로고
    • On the singularities of convex functions
    • Alberti, G., Ambrosio, L., Cannarsa, P.: On the singularities of convex functions. Manuscr. Math. 76 (1992), 421-435
    • (1992) Manuscr. Math. , vol.76 , pp. 421-435
    • Alberti, G.1    Ambrosio, L.2    Cannarsa, P.3
  • 3
    • 0001246518 scopus 로고
    • On the first variation of a varifold
    • Allard, W. K.: On the first variation of a varifold. Ann. Math. 95 (1972), 417-491
    • (1972) Ann. Math. , vol.95 , pp. 417-491
    • Allard, W.K.1
  • 4
    • 84972535466 scopus 로고
    • Convex functions and upper semi-continuous collections
    • Anderson, R. D., Klee, V. L.: Convex functions and upper semi-continuous 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
  • 5
    • 51249161652 scopus 로고
    • Singular sets of convex bodies and surfaces with generalized curvatures
    • Anzellotti, G., Ossanna, E.: Singular sets of convex bodies and surfaces with generalized curvatures. Manuscr. Math. 86 (1995), 417-433
    • (1995) Manuscr. Math. , vol.86 , pp. 417-433
    • Anzellotti, G.1    Ossanna, E.2
  • 7
    • 0001798574 scopus 로고
    • Sets with positive reach
    • Bangert, V.: Sets with positive reach. Arch. Math. 38 (1982), 54-57
    • (1982) Arch. Math. , vol.38 , pp. 54-57
    • Bangert, V.1
  • 8
    • 0004179050 scopus 로고
    • Birkhäuser Boston, Boston
    • Cohn, D. L.: Measure Theory. Birkhäuser Boston, Boston 1980
    • (1980) Measure Theory
    • Cohn, D.L.1
  • 9
    • 0031285893 scopus 로고    scopus 로고
    • Qualitative and quantitative results for sets of singular points of convex bodies
    • Colesanti, A., Pucci, C.: Qualitative and quantitative results for sets of singular points of convex bodies. Forum Math. 9 (1997), 103-125
    • (1997) Forum Math. , vol.9 , pp. 103-125
    • Colesanti, A.1    Pucci, C.2
  • 11
    • 0000515079 scopus 로고
    • On the second derivatives of convex functions
    • Dudley, R. M.: On the second derivatives of convex functions. Math. Scand. 41 (1977), 159-174
    • (1977) Math. Scand. , vol.41 , pp. 159-174
    • Dudley, R.M.1
  • 14
    • 84972563523 scopus 로고
    • Tubular neighborhoods in Euclidean spaces
    • Fu, J. H. G.: Tubular neighborhoods in Euclidean spaces. Duke Math. J. 52 (1985), 1025-1046
    • (1985) Duke Math. J. , vol.52 , pp. 1025-1046
    • Fu, J.H.G.1
  • 16
    • 0002278455 scopus 로고
    • Baire categories in convexity
    • ed. by P. M. Gruber & J. M. Wills. North-Holland, Amsterdam
    • Gruber, P. M.: Baire Categories in Convexity. In Handbook of Convex Geometry, ed. by P. M. Gruber & J. M. Wills. North-Holland, Amsterdam, 1993, 1327-1346
    • (1993) Handbook of Convex Geometry , pp. 1327-1346
    • Gruber, P.M.1
  • 17
    • 0000948005 scopus 로고    scopus 로고
    • Curvature relations and affine surface area for a general convex body and its polar
    • Hug, D.: Curvature relations and affine surface area for a general convex body and its polar. Result. Math. 29 (1996), 233-248
    • (1996) Result. Math. , vol.29 , pp. 233-248
    • Hug, D.1
  • 18
    • 0001466381 scopus 로고
    • On the mean number of normals through a point in the interior of a convex body
    • Hug, D.: On the mean number of normals through 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
  • 19
    • 0002204697 scopus 로고
    • Some new results on smoothness and rotundity in normed linear spaces
    • Klee, V.: Some new results on smoothness and rotundity in normed linear spaces. Math. Ann. 139 (1959), 51-63
    • (1959) Math. Ann. , vol.139 , pp. 51-63
    • Klee, V.1
  • 20
    • 0000644398 scopus 로고
    • Curvature measures and steiner formulae in space forms
    • Kohlmann, P.: Curvature measures and Steiner formulae in space forms. Geom. Dedicata 40 (1991), 191-211
    • (1991) Geom. Dedicata , vol.40 , pp. 191-211
    • Kohlmann, P.1
  • 22
    • 0013555830 scopus 로고
    • Comparison between the generalized mean curvature according to Allard and Federer's mean curvature measure
    • Ossanna, E.: Comparison between the generalized mean curvature according to Allard and Federer's mean curvature measure. Rend. Semin. Mat. Univ. Padova 88 (1992), 221-227
    • (1992) Rend. Semin. Mat. Univ. Padova , vol.88 , pp. 221-227
    • Ossanna, E.1
  • 24
    • 0003333144 scopus 로고
    • Convex bodies: The Brunn-Minkowski theory
    • Cambridge University Press, Cambridge
    • Schneider, R.: Convex Bodies: the Brunn-Minkowski Theory. Encyclopedia of Mathematics and its Applications 44. Cambridge University Press, Cambridge 1993
    • (1993) Encyclopedia of Mathematics and Its Applications , vol.44
    • Schneider, R.1
  • 26
    • 0002222913 scopus 로고
    • Random processes of Hausdorff rectifiable closed sets
    • Zähle, M.: Random processes of Hausdorff rectifiable closed sets. Math. Nachr. 108 (1982), 49-72
    • (1982) Math. Nachr. , vol.108 , pp. 49-72
    • Zähle, M.1
  • 27
    • 0000182794 scopus 로고
    • Integral and current representation of Federer's curvature measures
    • Zähle, M.: Integral and current representation of Federer's curvature measures. Arch. Math. 46 (1986), 557-567
    • (1986) Arch. Math. , vol.46 , pp. 557-567
    • Zähle, M.1
  • 28
    • 0000884525 scopus 로고
    • On the differentiation of convex functions in finite and infinite dimensional spaces Czech
    • Zajiĉek, L.: On the differentiation of convex functions in finite and infinite dimensional spaces Czech. Math. J. 29 (1979), 340-348
    • (1979) Math. J. , vol.29 , pp. 340-348
    • Zajiĉek, L.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.