메뉴 건너뛰기




Volumn 101, Issue 2, 2000, Pages 209-238

Hessian measures of semi-convex functions and applications to support measures of convex bodies

Author keywords

[No Author keywords available]

Indexed keywords


EID: 0034347243     PISSN: 00252611     EISSN: None     Source Type: Journal    
DOI: 10.1007/s002290050015     Document Type: Article
Times cited : (37)

References (44)
  • 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. Partial Differential Equations 2, 17-27 (1994)
    • (1994) Calc. Var. Partial Differential Equations , vol.2 , pp. 17-27
  • 3
    • 0000287587 scopus 로고    scopus 로고
    • Description of continuous isometry covariant valuations on convex sets
    • Alesker, S.: Description of continuous isometry covariant valuations on convex sets. Geom. Dedicata 74, 241-248 (1999)
    • (1999) Geom. Dedicata , vol.74 , pp. 241-248
    • Alesker, S.1
  • 4
    • 0033416837 scopus 로고    scopus 로고
    • Continuous rotation invariant valuations on convex sets
    • Alesker, S.: Continuous rotation invariant valuations on convex sets. Ann. of Math. 149, 977-1005 (1999)
    • (1999) Ann. of Math. , vol.149 , pp. 977-1005
    • Alesker, S.1
  • 5
    • 51249161652 scopus 로고
    • Singular sets of convex bodies and surfaces with generalized curvatures
    • Anzellotti, G. and Ossanna, E.: Singular sets of convex bodies and surfaces with generalized curvatures. Manuscripta Math. 86, 417-433 (1995)
    • (1995) Manuscripta Math. , vol.86 , pp. 417-433
    • Anzellotti, G.1    Ossanna, E.2
  • 7
    • 84941449805 scopus 로고
    • Analytische Eigenschaften konvexer Funktionen auf Riemannschen Mannigfaltigkeiten
    • Bangert, V.: Analytische Eigenschaften konvexer Funktionen auf Riemannschen Mannigfaltigkeiten. J. Reine Angew. Math. 307/308, 309-324 (1979)
    • (1979) J. Reine Angew. Math. , vol.307-308 , pp. 309-324
    • Bangert, V.1
  • 8
    • 0001798574 scopus 로고
    • Sets with positive reach
    • Bangert, V.: Sets with positive reach. Arch. Math. 38, 54-57 (1982)
    • (1982) Arch. Math. , vol.38 , pp. 54-57
    • Bangert, V.1
  • 9
    • 38249027172 scopus 로고
    • On p-convex sets and geodesics
    • Canino, A.: On p-convex sets and geodesics. J. Differential Equations 75, 118-157 (1988)
    • (1988) J. Differential Equations , vol.75 , pp. 118-157
    • Canino, A.1
  • 10
    • 0001941035 scopus 로고
    • Local properties of geodesics on p-convex sets
    • Canino, A.: Local properties of geodesics on p-convex sets, Ann. Mat. Pura Appl. 49, 17-44 (1991)
    • (1991) Ann. Mat. Pura Appl. , vol.49 , pp. 17-44
    • Canino, A.1
  • 11
    • 0003859933 scopus 로고
    • Canadian Mathematical Society, Wiley-Interscience Publication, New York
    • Clarke, F.H.: Optimization and Nonsmooth Analysis. Canadian Mathematical Society, Wiley-Interscience Publication, New York, 1983
    • (1983) Optimization and Nonsmooth Analysis
    • Clarke, F.H.1
  • 13
    • 3042877473 scopus 로고    scopus 로고
    • A Steiner type formula for convex functions
    • Colesanti, A.: A Steiner type formula for convex functions. Mathematika 44, 195-214 (1997)
    • (1997) Mathematika , vol.44 , pp. 195-214
    • Colesanti, A.1
  • 14
    • 85037752454 scopus 로고    scopus 로고
    • Steiner type formulae and weighted measures of singularities for semi-convex functions
    • To appear in
    • Colesanti, A. and Hug, D.: Steiner type formulae and weighted measures of singularities for semi-convex functions. To appear in Trans. Amer. Math. Soc.
    • Trans. Amer. Math. Soc.
    • Colesanti, A.1    Hug, D.2
  • 15
    • 0031521507 scopus 로고    scopus 로고
    • Generalised solutions of Hessian equations
    • Colesanti, A. and Salani, P.: Generalised solutions of Hessian equations. Bull. Austral. Math. Soc. 56, 459-466 (1997)
    • (1997) Bull. Austral. Math. Soc. , vol.56 , pp. 459-466
    • Colesanti, A.1    Salani, P.2
  • 16
    • 0001515891 scopus 로고    scopus 로고
    • Quermaßdichten für Punktprozesse konvexer Körper und Boolesche Modelle
    • Fallert, H.: Quermaßdichten für Punktprozesse konvexer Körper und Boolesche Modelle. Math. Nachr. 181, 165-184 (1996)
    • (1996) Math. Nachr. , vol.181 , pp. 165-184
    • Fallert, H.1
  • 19
    • 84972563523 scopus 로고
    • Tubular neighborhoods in Euclidean spaces
    • Fu, J.H.G.: Tubular neighborhoods in Euclidean spaces. Duke Math. J. 52, 1025-1046 (1985)
    • (1985) Duke Math. J. , vol.52 , pp. 1025-1046
    • Fu, J.H.G.1
  • 20
    • 0000477192 scopus 로고
    • Monge-ampère functions, I
    • Fu, J.H.G.: Monge-Ampère functions, I. Indiana Univ. Math. J. 38, 745-771 (1989)
    • (1989) Indiana Univ. Math. J. , vol.38 , pp. 745-771
    • Fu, J.H.G.1
  • 21
    • 0000477192 scopus 로고
    • Monge-Ampère functions, II
    • Fu, J.H.G.: Monge-Ampère functions, II. Indiana Univ. Math. J. 38, 773-789 (1989)
    • (1989) Indiana Univ. Math. J. , vol.38 , pp. 773-789
    • Fu, J.H.G.1
  • 22
  • 26
    • 0000490508 scopus 로고    scopus 로고
    • Functional analytic characterizations of classes of convex bodies
    • Goodey, P., Lutwak, E. and Weil, W.: Functional analytic characterizations of classes of convex bodies. Math. Z. 222, 363-381 (1996)
    • (1996) Math. Z. , vol.222 , pp. 363-381
    • Goodey, P.1    Lutwak, E.2    Weil, W.3
  • 27
    • 0002517837 scopus 로고
    • Zonoids and generalizations
    • P. M. Gruber and J. M. Wills (eds). Vol. B, North Holland, Amsterdam
    • Goodey, P. and Weil, W.: Zonoids and generalizations. In: Handbook of convex geometry, P. M. Gruber and J. M. Wills (eds). Vol. B, North Holland, Amsterdam, 1993, pp. 1297-1326
    • (1993) In: Handbook of Convex Geometry , pp. 1297-1326
    • Goodey, P.1    Weil, W.2
  • 28
    • 0032221844 scopus 로고    scopus 로고
    • Generalized curvature measures and singularities of sets with positive reach
    • Hug, D.: Generalized curvature measures and singularities of sets with positive reach. Forum Math. 10, 699-728 (1998)
    • (1998) Forum Math. , vol.10 , pp. 699-728
    • Hug, D.1
  • 29
    • 0033482136 scopus 로고    scopus 로고
    • Absolute continuity for curvature measures of convex sets II
    • Hug, D.: Absolute continuity for curvature measures of convex sets II. Math. Z. 232, 437-485 (1999)
    • (1999) Math. Z. , vol.232 , pp. 437-485
    • Hug, D.1
  • 31
    • 0002824461 scopus 로고
    • Viscosity solutions of fully nonlinear second-order elliptic partial differential equations
    • Ishii, H. and Lions, P.L.: Viscosity solutions of fully nonlinear second-order elliptic partial differential equations. J. Differential Equations 83, 26-78 (1990)
    • (1990) J. Differential Equations , vol.83 , pp. 26-78
    • Ishii, H.1    Lions, P.L.2
  • 32
    • 0002084725 scopus 로고
    • Sur une classe de fonctions sous-linéarisables
    • Janin, R.: Sur une classe de fonctions sous-linéarisables. C. R. Acad. Sci. Paris Sér. I Math. 277, 265-267 (1973)
    • (1973) C. R. Acad. Sci. Paris Sér. I Math. , vol.277 , pp. 265-267
    • Janin, R.1
  • 33
    • 0002339515 scopus 로고
    • Nächste punkte in der riemannschen geometrie
    • Kleinjohann, N.: Nächste Punkte in der Riemannschen Geometrie. Math. Z. 176, 327-344 (1981)
    • (1981) Math. Z. , vol.176 , pp. 327-344
    • Kleinjohann, N.1
  • 34
    • 0004267646 scopus 로고
    • Princeton University Press, Princeton
    • Rockafellar, R.: Convex Analysis. Princeton University Press, Princeton, 1970
    • (1970) Convex Analysis
    • Rockafellar, R.1
  • 37
    • 0001358583 scopus 로고
    • Convex surfaces, curvature and surface area measures
    • P. M. Gruber and J. M. Wills (eds), V North Holland, Amsterdam
    • Schneider, R.: Convex surfaces, curvature and surface area measures. In: Handbook of convex geometry, P. M. Gruber and J. M. Wills (eds), Vol. A, North Holland, Amsterdam, 1993, pp. 273-299
    • (1993) Handbook of Convex Geometry , vol.A , pp. 273-299
    • Schneider, R.1
  • 38
    • 21344466360 scopus 로고    scopus 로고
    • Simple valuations on convex bodies
    • Schneider, R.: Simple valuations on convex bodies. Mathematika 43, 32-39 (1996)
    • (1996) Mathematika , vol.43 , pp. 32-39
    • Schneider, R.1
  • 39
    • 0002675053 scopus 로고
    • Integral geometry
    • P. M. Gruber and J. M. Wills (eds), North Holland, Amsterdam
    • Schneider, R. and Wieacker, J.A.: Integral geometry. In: Handbook of convex geometry, P. M. Gruber and J. M. Wills (eds), Vol. B. North Holland, Amsterdam, 1993, pp. 1349-1390
    • (1993) Handbook of Convex Geometry , vol.B , pp. 1349-1390
    • Schneider, R.1    Wieacker, J.A.2
  • 44
    • 0002339517 scopus 로고    scopus 로고
    • Generalised Hessian, Max function and weak convexity
    • Yang, X.Q.: Generalised Hessian, Max function and weak convexity. Bull. Austral. Math. Soc. 53, 21-32 (1996)
    • (1996) Bull. Austral. Math. Soc. , vol.53 , pp. 21-32
    • Yang, X.Q.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.