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Volumn 7, Issue 3, 1997, Pages 535-560

Kirszbraun's theorem and metric spaces of bounded curvature

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EID: 0031285540     PISSN: 1016443X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s000390050018     Document Type: Article
Times cited : (112)

References (34)
  • 1
    • 0010757593 scopus 로고
    • The circumdisk and its relation to a theorem of Kirszbraun and Valentine
    • R. ALEXANDER, The circumdisk and its relation to a theorem of Kirszbraun and Valentine, Math. Mag. 57 (1984), 165-169.
    • (1984) Math. Mag. , vol.57 , pp. 165-169
    • Alexander, R.1
  • 2
    • 0001726657 scopus 로고
    • The Hadamard-Cartan theorem in locally convex metric spaces
    • S.B. ALEXANDER, R.L. BISHOP, The Hadamard-Cartan theorem in locally convex metric spaces, Enseign. Math. 36 (1990), 309-320.
    • (1990) Enseign. Math. , vol.36 , pp. 309-320
    • Alexander, S.B.1    Bishop, R.L.2
  • 6
    • 0010673961 scopus 로고
    • Noyaux de kirszbraun et distances de hellinger
    • P. ASSOUAD, Noyaux de Kirszbraun et distances de Hellinger, C. R. Acad. Sci. Paris 297 (1983), 623-626.
    • (1983) C. R. Acad. Sci. Paris , vol.297 , pp. 623-626
    • Assouad, P.1
  • 7
    • 0000893870 scopus 로고
    • Markov chains, Riesz transforms and Lipschitz maps
    • K. BALL, Markov chains, Riesz transforms and Lipschitz maps, Geometry And Functional Analysis 2 (1992), 137-172.
    • (1992) Geometry and Functional Analysis , vol.2 , pp. 137-172
    • Ball, K.1
  • 8
    • 0003223423 scopus 로고
    • Lectures on spaces of nonpositive curvature
    • Birkhäuser, Basel
    • W. BALLMANN, Lectures on spaces of nonpositive curvature, DMV Seminar Band, no. 25, Birkhäuser, Basel, 1995.
    • (1995) DMV Seminar Band , vol.25
    • Ballmann, W.1
  • 10
    • 0010675664 scopus 로고
    • Spaces with bounded curvature and distance geometry
    • V.N. BERESTOVSKIJ, Spaces with bounded curvature and distance geometry, Siberian Math. J. 27 (1986), 8-19.
    • (1986) Siberian Math. J. , vol.27 , pp. 8-19
    • Berestovskij, V.N.1
  • 13
    • 33646864986 scopus 로고
    • A.D. Alexandrov spaces with curvature bounded below
    • Yu.D. BURAGO, M. GROMOV, G. PERELMAN, A.D. Alexandrov spaces with curvature bounded below, Russian Math. Surveys 47:2 (1992), 1-58.
    • (1992) Russian Math. Surveys , vol.47 , Issue.2 , pp. 1-58
    • Burago, Yu.D.1    Gromov, M.2    Perelman, G.3
  • 15
    • 0001751998 scopus 로고
    • Helly's theorem and its relatives
    • V. Klee, ed., Convexity, Amer. Math. Soc., Providence, R.I.
    • L. DANZER, B. GRÜNBAUM, V. KLEE, Helly's theorem and its relatives, in "Proceedings of Symposia in Pure Mathematics" (V. Klee, ed.), vol. 7, Convexity, Amer. Math. Soc., Providence, R.I. (1963), 101-180.
    • (1963) Proceedings of Symposia in Pure Mathematics , vol.7 , pp. 101-180
    • Danzer, L.1    Grünbaum, B.2    Klee, V.3
  • 16
    • 0010757594 scopus 로고
    • Ein erweiterungssatz für monotone mengen
    • H. DEBRUNNER, P. FLOR, Ein Erweiterungssatz für monotone Mengen, Arch. Math. 15 (1964), 445-447.
    • (1964) Arch. Math. , vol.15 , pp. 445-447
    • Debrunner, H.1    Flor, P.2
  • 18
    • 0003195390 scopus 로고
    • Hyperbolic groups
    • S.M. Gersten, ed., MSRI Publ. no. 8, Springer
    • M. GROMOV, Hyperbolic groups, in "Essays in group theory" (S.M. Gersten, ed.), MSRI Publ. no. 8, Springer (1987), 75-263.
    • (1987) Essays in Group Theory , pp. 75-263
    • Gromov, M.1
  • 19
    • 0002874575 scopus 로고
    • Asymptotic invariants of infinite groups
    • "Geometric group theory" (G.A. Niblo, M.A. Roller, eds.), Cambridge Univ. Press
    • M. GROMOV, Asymptotic invariants of infinite groups, in "Geometric group theory" (G.A. Niblo, M.A. Roller, eds.), vol. 2, London Math. Soc. Lecture Notes Series no. 182, Cambridge Univ. Press (1993), 1-295.
    • (1993) London Math. Soc. Lecture Notes Series No. 182 , vol.2 , pp. 1-295
    • Gromov, M.1
  • 20
    • 0010758928 scopus 로고
    • A generalization of theorems of Kirszbraun and Minty
    • B. GRÜNBAUM, A generalization of theorems of Kirszbraun and Minty, Proc. Amer. Math. Soc. 13 (1962), 812-814.
    • (1962) Proc. Amer. Math. Soc. , vol.13 , pp. 812-814
    • Grünbaum, B.1
  • 21
    • 0010718388 scopus 로고
    • Extension and selection problems for nonlinear semigroups in Banach spaces
    • M.M. ISRAEL, S. REICH, Extension and selection problems for nonlinear semigroups in Banach spaces, Math. Japon. 28 (1983), 1-8.
    • (1983) Math. Japon. , vol.28 , pp. 1-8
    • Israel, M.M.1    Reich, S.2
  • 22
    • 0001654702 scopus 로고
    • Extensions of Lipschitz mappings into a Hilbert space
    • W.B. JOHNSON, J. LINDENSTRAUSS, Extensions of Lipschitz mappings into a Hilbert space, Contemp. Math. 26 (1984), 189-206.
    • (1984) Contemp. Math. , vol.26 , pp. 189-206
    • Johnson, W.B.1    Lindenstrauss, J.2
  • 23
    • 0001805162 scopus 로고
    • Über die zusammenziehende und lipschitzsche transformationen
    • M.D. KIRSZBRAUN, Über die zusammenziehende und Lipschitzsche Transformationen, Fundamente Math. 22 (1934), 77-108.
    • (1934) Fundamente Math. , vol.22 , pp. 77-108
    • Kirszbraun, M.D.1
  • 24
    • 0010677376 scopus 로고
    • Extensions of nonexpansive mappings in the Hilbert ball with the hyperbolic metric I, II
    • T. KUCZUMOW, A. STACHURA, Extensions of nonexpansive mappings in the Hilbert ball with the hyperbolic metric I, II, Comment. Math. Univ. Carolin. 29 (1988), 399-402, 403-410.
    • (1988) Comment. Math. Univ. Carolin. , vol.29 , pp. 399-402
    • Kuczumow, T.1    Stachura, A.2
  • 26
    • 84923279813 scopus 로고
    • Extension of range of functions
    • E.J. MCSHANE, Extension of range of functions, Bull. Amer. Math. Soc. 40 (1934), 837-842.
    • (1934) Bull. Amer. Math. Soc. , vol.40 , pp. 837-842
    • Mcshane, E.J.1
  • 27
    • 84966253469 scopus 로고
    • On the extension of Lipschitz, Lipschitz-Hölder continuous, and monotone operators
    • G.J. MINTY, On the extension of Lipschitz, Lipschitz-Hölder continuous, and monotone operators, Bull. Amer. Math. Soc. 76 (1970), 334-339.
    • (1970) Bull. Amer. Math. Soc. , vol.76 , pp. 334-339
    • Minty, G.J.1
  • 28
    • 51249165801 scopus 로고
    • The tangent cone of an Aleksandrov space of curvature ≤ K
    • I.G. NIKOLAEV, The tangent cone of an Aleksandrov space of curvature ≤ K, Manuscripta Math. 86 (1995), 137-147.
    • (1995) Manuscripta Math. , vol.86 , pp. 137-147
    • Nikolaev, I.G.1
  • 29
    • 8744309187 scopus 로고    scopus 로고
    • Spaces of Wald-Berestovskii curvature bounded below
    • C. PLAUT, Spaces of Wald-Berestovskii curvature bounded below, J. Geom. Anal. 6 (1996), 113-134.
    • (1996) J. Geom. Anal. , vol.6 , pp. 113-134
    • Plaut, C.1
  • 30
    • 0000552029 scopus 로고
    • Inextensible mappings in a space of curvature no greater than K
    • YU.G. RESHETNYAK, Inextensible mappings in a space of curvature no greater than K, Siberian Math. J. 9 (1968), 683-689.
    • (1968) Siberian Math. J. , vol.9 , pp. 683-689
    • Reshetnyak, Yu.G.1
  • 31
    • 0000581074 scopus 로고
    • On a theorem of Kirszbraun and Valentine
    • I.J. SCHOENBERG, On a theorem of Kirszbraun and Valentine, Amer. Math. Monthly 60 (1953), 620-622.
    • (1953) Amer. Math. Monthly , vol.60 , pp. 620-622
    • Schoenberg, I.J.1
  • 32
    • 0001807117 scopus 로고
    • A Lipschitz condition preserving extension for a vector function
    • F. A. VALENTINE, A Lipschitz condition preserving extension for a vector function, Amer. J. Math. 67 (1945), 83-93.
    • (1945) Amer. J. Math. , vol.67 , pp. 83-93
    • Valentine, F.A.1
  • 33
    • 0010723083 scopus 로고
    • Contractions in non-Euclidean spaces
    • F.A. VALENTINE, Contractions in non-Euclidean spaces, Bull. Amer. Math. Soc. 50 (1944), 710-713.
    • (1944) Bull. Amer. Math. Soc. , vol.50 , pp. 710-713
    • Valentine, F.A.1
  • 34
    • 0010718675 scopus 로고
    • Begründung einer koordinatenlosen differentialgeometrie der flächen
    • Wien
    • A. WALD, Begründung einer koordinatenlosen Differentialgeometrie der Flächen, Ergebnisse eines math. Kolloquiums, Wien 7 (1935), 24-46.
    • (1935) Ergebnisse Eines Math. Kolloquiums , vol.7 , pp. 24-46
    • Wald, A.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.