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Volumn 13, Issue 3, 2001, Pages 339-376

Surface measures in Carnot-Carathéodory spaces

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EID: 0012592396     PISSN: 09442669     EISSN: None     Source Type: Journal    
DOI: 10.1007/s005260000076     Document Type: Article
Times cited : (137)

References (56)
  • 4
    • 85037781488 scopus 로고    scopus 로고
    • Rectifiable sets in metric and Banach spaces
    • to appear
    • L. Ambrosio, B. Kirchheim, Rectifiable sets in metric and Banach spaces, to appear on Math. Ann.
    • Math. Ann.
    • Ambrosio, L.1    Kirchheim, B.2
  • 7
    • 34748925841 scopus 로고
    • Approximation of functionals depending on jumps by elliptic functionals via Γ-convergence
    • L. Ambrosio, V.M. Tortorelli, Approximation of functionals depending on jumps by elliptic functionals via Γ-convergence, Comm. Pure Appl. Math. 43 (1990), 999-1036
    • (1990) Comm. Pure Appl. Math. , vol.43 , pp. 999-1036
    • Ambrosio, L.1    Tortorelli, V.M.2
  • 8
    • 84935168793 scopus 로고
    • Minimal interface criterion for phase transitions in mixtures of Cahn-Hilliard fluids
    • S. Baldo, Minimal interface criterion for phase transitions in mixtures of Cahn-Hilliard fluids, Ann. Inst. H. Poincaré Anal. Non Linéaire 7 (1990), 67-90
    • (1990) Ann. Inst. H. Poincaré Anal. Non Linéaire , vol.7 , pp. 67-90
    • Baldo, S.1
  • 10
    • 0007299876 scopus 로고    scopus 로고
    • Some results in surface measure in Calculus of Variations
    • G. Bellettini, M. Paolini, S. Venturini, Some results in surface measure in Calculus of Variations, Ann.Mat.Pura Appl.(4) 170 (1996), 329-357
    • (1996) Ann.Mat.Pura Appl. , vol.170 , Issue.4 , pp. 329-357
    • Bellettini, G.1    Paolini, M.2    Venturini, S.3
  • 11
    • 84972530683 scopus 로고
    • Quasi-optimal error estimates for the mean curvature flow with a forcing term
    • G. Bellettini, M. Paolini, Quasi-optimal error estimates for the mean curvature flow with a forcing term, Differential Integral Equations 8 (1995), 735-752
    • (1995) Differential Integral Equations , vol.8 , pp. 735-752
    • Bellettini, G.1    Paolini, M.2
  • 13
    • 33846814955 scopus 로고
    • Singular perturbations of variational problems arising from a two-phase transition model
    • G. Bouchitté, Singular perturbations of variational problems arising from a two-phase transition model, Appl. Math. Optim. 21 (1990), 289-314
    • (1990) Appl. Math. Optim. , vol.21 , pp. 289-314
    • Bouchitté, G.1
  • 14
    • 0011354331 scopus 로고    scopus 로고
    • On differentiability of absolute continuous functions
    • A.P. Calderón, On differentiability of absolute continuous functions, Riv. Mat. Univ. Parma 2, 203-213
    • Riv. Mat. Univ. Parma , vol.2 , pp. 203-213
    • Calderón, A.P.1
  • 15
    • 0001189770 scopus 로고
    • The geometric Sobolev embedding for vector fields and the isoperimetric inequality
    • L. Capogna, D. Danielli, N. Garofalo, The geometric Sobolev embedding for vector fields and the isoperimetric inequality, Comm. Anal. Geom. 12 (1994), 203-215
    • (1994) Comm. Anal. Geom. , vol.12 , pp. 203-215
    • Capogna, L.1    Danielli, D.2    Garofalo, N.3
  • 16
    • 0033456306 scopus 로고    scopus 로고
    • Differentiability of Lipschitz functions on metric measure spaces
    • J. Cheeger, Differentiability of Lipschitz functions on metric measure spaces, Geometry and Functional Analysis 9 (1999), 428-517
    • (1999) Geometry and Functional Analysis , vol.9 , pp. 428-517
    • Cheeger, J.1
  • 18
    • 0000014518 scopus 로고    scopus 로고
    • Traces inequalities for Carnot-Carathèoodory spaces and applications
    • D. Danielli, N. Garofalo, D.M. Nhieu, Traces inequalities for Carnot-Carathèoodory spaces and applications, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 27 (1998), 195-252
    • (1998) Ann. Scuola Norm. Sup. Pisa Cl. Sci. , vol.27 , Issue.4 , pp. 195-252
    • Danielli, D.1    Garofalo, N.2    Nhieu, D.M.3
  • 20
    • 0002837504 scopus 로고
    • Problema di Plateau generale e funzionali geodetici
    • E. De Giorgi, Problema di Plateau generale e funzionali geodetici, Atti Sem. Mat. Fis. Univ. Modena 43 (1995), 285-292
    • (1995) Atti Sem. Mat. Fis. Univ. Modena , vol.43 , pp. 285-292
    • De Giorgi, E.1
  • 25
    • 0001010690 scopus 로고
    • Sobolev and isoperimetric inequalities for degenerate metrics
    • B. Franchi, S. Gallot, R.L. Wheeden, Sobolev and isoperimetric inequalities for degenerate metrics, Math. Ann. 300 (1994), 557-571
    • (1994) Math. Ann. , vol.300 , pp. 557-571
    • Franchi, B.1    Gallot, S.2    Wheeden, R.L.3
  • 26
    • 0000541936 scopus 로고
    • Hölder regularity theorem for a class of non uniformly elliptic operators with measurable coefficients
    • B. Franchi, E. Lanconelli, Hölder regularity theorem for a class of non uniformly elliptic operators with measurable coefficients. Ann. Scuola Norm. Sup. Pisa 10 (1983), 523-541
    • (1983) Ann. Scuola Norm. Sup. Pisa , vol.10 , pp. 523-541
    • Franchi, B.1    Lanconelli, E.2
  • 27
    • 0001594749 scopus 로고    scopus 로고
    • Meyers-Serrin Type Theorems and Relaxation of Variational Integrals Depending Vector Fields
    • B. Franchi, R. Serapioni, F. Serra Cassano, Meyers-Serrin Type Theorems and Relaxation of Variational Integrals Depending Vector Fields, Houston Journal of Mathematics 22 (1996), 859-889
    • (1996) Houston Journal of Mathematics , vol.22 , pp. 859-889
    • Franchi, B.1    Serapioni, R.2    Serra Cassano, F.3
  • 28
    • 0002805615 scopus 로고    scopus 로고
    • Approximation and Imbedding Theorems for Weighted Sobolev Spaces Associated with Lipschitz Continuous Vector Fields
    • B. Franchi, R. Serapioni, F. Serra Cassano, Approximation and Imbedding Theorems for Weighted Sobolev Spaces Associated with Lipschitz Continuous Vector Fields, Bollettino U.M.I., 7 11-B (1997), 83-117
    • (1997) Bollettino U.M.I. , vol.11 B , Issue.7 , pp. 83-117
    • Franchi, B.1    Serapioni, R.2    Serra Cassano, F.3
  • 30
    • 0030488404 scopus 로고    scopus 로고
    • Isoperimetric and Sobolev inequalities for Carnot-Carathéodory spaces and the existence of minimal surfaces
    • N. Garofalo, D.M. Nhieu, Isoperimetric and Sobolev inequalities for Carnot-Carathéodory spaces and the existence of minimal surfaces, Comm. Pure Appl. Math. 49 (1996), 1081-1144
    • (1996) Comm. Pure Appl. Math. , vol.49 , pp. 1081-1144
    • Garofalo, N.1    Nhieu, D.M.2
  • 31
    • 0032410775 scopus 로고    scopus 로고
    • Lipschitz continuity, global smooth approximations and extension theorems for Sobolev functions in Carnot Carathéodory spaces
    • N. Garofalo, D.M. Nhieu, Lipschitz continuity, global smooth approximations and extension theorems for Sobolev functions in Carnot Carathéodory spaces, Jour. Analyse Mathematique 74 (1998), 67-97
    • (1998) Jour. Analyse Mathematique , vol.74 , pp. 67-97
    • Garofalo, N.1    Nhieu, D.M.2
  • 33
    • 0002299742 scopus 로고    scopus 로고
    • Carnot-Caratheódory spaces seen from within
    • ed. by A. Bellaïche and J. Risler, Birkhäuser, Basel
    • M. Gromov, Carnot-Caratheódory spaces seen from within, in Sub-Riemannian Geometry, Progress in Mathematics 144. ed. by A. Bellaïche and J. Risler, Birkhäuser, Basel, 1996
    • (1996) Sub-Riemannian Geometry, Progress in Mathematics , vol.144
    • Gromov, M.1
  • 37
    • 15244346736 scopus 로고
    • Hypoelliptic second-order differential equations
    • L. Hörmander, Hypoelliptic second-order differential equations, Acta Math. 121 (1968), 147-171
    • (1968) Acta Math. , vol.121 , pp. 147-171
    • Hörmander, L.1
  • 38
    • 0001993902 scopus 로고
    • Subelliptic, second order differential operators
    • Springer
    • D. Jerison, A. Sanchez Calle, Subelliptic, second order differential operators, in Complex analysis III, Springer, 1987, 46-77
    • (1987) Complex Analysis , vol.3 , pp. 46-77
    • Jerison, D.1    Sanchez Calle, A.2
  • 41
    • 0346540343 scopus 로고    scopus 로고
    • Differentiability and area formula on Carnot groups
    • to appear
    • V. Magnani, Differentiability and area formula on Carnot groups, to appear on Houston Journal of Mathematics
    • Houston Journal of Mathematics
    • Magnani, V.1
  • 44
    • 84972526602 scopus 로고
    • On Carnot-Carathèodory metrics
    • J. Mitchell, On Carnot-Carathèodory metrics, J.Differ. Geom. 21 (1985), 35-45
    • (1985) J.Differ. Geom. , vol.21 , pp. 35-45
    • Mitchell, J.1
  • 46
    • 34250109116 scopus 로고
    • The gradient theory of phase transitions and the minimal interface criterion
    • L. Modica, The gradient theory of phase transitions and the minimal interface criterion. Arch. Rational Mech. Anal. 98 (1987), 123-142
    • (1987) Arch. Rational Mech. Anal. , vol.98 , pp. 123-142
    • Modica, L.1
  • 47
    • 0012990431 scopus 로고
    • II limite nella F-convergenza di una famiglia di funzionali ellittici
    • L. Modica, S. Mortola, II limite nella F-convergenza di una famiglia di funzionali ellittici, Boll. Un. Mat. Ital. A (5) 14 (1977), 526-529
    • (1977) Boll. Un. Mat. Ital. A , vol.14 , Issue.5 , pp. 526-529
    • Modica, L.1    Mortola, S.2
  • 48
    • 0345909279 scopus 로고    scopus 로고
    • Some properties of Carnot-Carathéodory balls in the Heisenberg group
    • to appear
    • R. Monti, Some properties of Carnot-Carathéodory balls in the Heisenberg group, to appear on Rend. Mat. Acc. Lincei
    • Rend. Mat. Acc. Lincei
    • Monti, R.1
  • 49
    • 0041862120 scopus 로고
    • Balls and metrics defined by vector fields I: Basic properties
    • A. Nagel, E.M. Stein, S. Wainger, Balls and metrics defined by vector fields I: Basic properties, Acta Math. 155 (1985), 103-147
    • (1985) Acta Math. , vol.155 , pp. 103-147
    • Nagel, A.1    Stein, E.M.2    Wainger, S.3
  • 50
    • 0001773527 scopus 로고
    • Métriques de Carnot-Carathéodory et quasiisométries des espaces symétriques de rang un
    • P. Pansu, Métriques de Carnot-Carathéodory et quasiisométries des espaces symétriques de rang un, Annals of Mathematics 129 (1989), 1-60
    • (1989) Annals of Mathematics , vol.129 , pp. 1-60
    • Pansu, P.1
  • 51
    • 0001641428 scopus 로고
    • Une inégalité isopérimétrique sur Ie groupe de Heisenberg
    • P. Pansu, Une inégalité isopérimétrique sur Ie groupe de Heisenberg, C.R. Acad. Sci. Paris 295, I, (1982), 127-130
    • (1982) C.R. Acad. Sci. Paris , vol.295 , Issue.1 , pp. 127-130
    • Pansu, P.1
  • 53
    • 34250382135 scopus 로고
    • Hypoelliptic differential operators and nilpotent groups
    • L. Rothschild, E.M. Stein, Hypoelliptic differential operators and nilpotent groups, Acta Math. 137 (1976), 247-320
    • (1976) Acta Math. , vol.137 , pp. 247-320
    • Rothschild, L.1    Stein, E.M.2
  • 56
    • 0011328164 scopus 로고    scopus 로고
    • Approximately differentiable transformations and the change of variables on nilpotent groups
    • S.K. Vodopjanov, A.D. Ukhlov, Approximately differentiable transformations and the change of variables on nilpotent groups, Sibirsk. Mat. Zh. 37 (1996), 70-89
    • (1996) Sibirsk. Mat. Zh. , vol.37 , pp. 70-89
    • Vodopjanov, S.K.1    Ukhlov, A.D.2


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