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Remarks on multi-marginal symmetric Monge-Kantorovich problems
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Metric cycles, curves and solenoids
1. | Dipartimento di Matematica "L. Tonelli", Università di Pisa, Largo B. Pontecorvo 5, 56127 Pisa, Italy |
2. | St.Petersburg Branch of the Steklov Mathematical Institute, of the Russian Academy of Sciences, Fontanka 27, 191023 St.Petersburg, Russian Federation |
References:
[1] |
L. Ambrosio and B. Kirchheim, Currents in metric spaces, Acta Math., 185 (2000), 1-80.
doi: 10.1007/BF02392711. |
[2] |
L. Ambrosio and P. Tilli, "Topics on Analysis in Metric Spaces,'' Oxford Lecture Series in Mathematics and its Applications, 25, Oxford University Press, Oxford, 2004. |
[3] |
V. Bangert, Minimal measures and minimizing closed normal one-currents, Geom. Funct. Anal., 9 (1999), 413-427.
doi: 10.1007/s000390050093. |
[4] |
V. Bogachev, "Measure Theory. Vol. I, II," Springer-Verlag, Berlin, 2007.
doi: 10.1007/978-3-540-34514-5. |
[5] |
L. De Pascale, M. S. Gelli and L. Granieri, Minimal measures, one-dimensional currents and the Monge-Kantorovich problem, Calc. Var. Partial Differential Equations, 27 (2006), 1-23.
doi: 10.1007/s00526-006-0017-1. |
[6] |
M. B. Dubashinskiĭ, On uniform approximation by harmonic and almost harmonic vector fields, (in Russian), Zap. Nauchn. Sem. S.-Peterburg. Otdel. Mat. Inst. Steklov. (POMI), 389 (2011), Issledovaniya po Lineinym Operatoram i Teorii Funktsii., 38 (2011), 58-84.
doi: 10.1007/s10958-012-0766-7. |
[7] |
V. Muñoz and R. Pérez Marco, Ergodic solenoidal homology. II. Density of ergodic solenoids, Aust. J. Math. Anal. Appl., 6 (2009), 1-8. |
[8] |
V. Muñoz and R. Pérez Marco, Schwartzman cycles and ergodic solenoids, preprint, arXiv:0910.2837, (2009). |
[9] |
V. Muñoz and R. Pérez-Marco, Ergodic solenoidal homology: Realization theorem, Comm. Math. Phys., 302 (2011), 737-753.
doi: 10.1007/s00220-010-1183-8. |
[10] |
V. Muñoz and R. Pérez Marco, Ergodic solenoids and generalized currents, Rev. Mat. Complut., 24 (2011), 493-525.
doi: 10.1007/s13163-010-0050-7. |
[11] |
E. Paolini and E. Stepanov, Decomposition of acyclic normal currents in a metric space, J. Funct. Anal., 263 (2012), 3358-3390.
doi: 10.1016/j.jfa.2012.08.009. |
[12] |
E. Paolini and E. Stepanov, Structure of metric cycles and normal one-dimensional currents, J. Funct. Anal., 264 (2013), 1269-1295.
doi: 10.1016/j.jfa.2012.12.007. |
[13] |
S. Schwartzman, Asymptotic cycles, Ann. of Math. (2), 66 (1957), 270-284.
doi: 10.2307/1969999. |
[14] |
S. Schwartzman, Asymptotic cycles on non-compact spaces, Bull. London Math. Soc., 29 (1997), 350-352.
doi: 10.1112/S0024609396002561. |
[15] |
S. K. Smirnov, Decomposition of solenoidal vector charges into elementary solenoids and the structure of normal one-dimensional flows, St. Petersburg Math. J., 5 (1994), 841-867. |
show all references
References:
[1] |
L. Ambrosio and B. Kirchheim, Currents in metric spaces, Acta Math., 185 (2000), 1-80.
doi: 10.1007/BF02392711. |
[2] |
L. Ambrosio and P. Tilli, "Topics on Analysis in Metric Spaces,'' Oxford Lecture Series in Mathematics and its Applications, 25, Oxford University Press, Oxford, 2004. |
[3] |
V. Bangert, Minimal measures and minimizing closed normal one-currents, Geom. Funct. Anal., 9 (1999), 413-427.
doi: 10.1007/s000390050093. |
[4] |
V. Bogachev, "Measure Theory. Vol. I, II," Springer-Verlag, Berlin, 2007.
doi: 10.1007/978-3-540-34514-5. |
[5] |
L. De Pascale, M. S. Gelli and L. Granieri, Minimal measures, one-dimensional currents and the Monge-Kantorovich problem, Calc. Var. Partial Differential Equations, 27 (2006), 1-23.
doi: 10.1007/s00526-006-0017-1. |
[6] |
M. B. Dubashinskiĭ, On uniform approximation by harmonic and almost harmonic vector fields, (in Russian), Zap. Nauchn. Sem. S.-Peterburg. Otdel. Mat. Inst. Steklov. (POMI), 389 (2011), Issledovaniya po Lineinym Operatoram i Teorii Funktsii., 38 (2011), 58-84.
doi: 10.1007/s10958-012-0766-7. |
[7] |
V. Muñoz and R. Pérez Marco, Ergodic solenoidal homology. II. Density of ergodic solenoids, Aust. J. Math. Anal. Appl., 6 (2009), 1-8. |
[8] |
V. Muñoz and R. Pérez Marco, Schwartzman cycles and ergodic solenoids, preprint, arXiv:0910.2837, (2009). |
[9] |
V. Muñoz and R. Pérez-Marco, Ergodic solenoidal homology: Realization theorem, Comm. Math. Phys., 302 (2011), 737-753.
doi: 10.1007/s00220-010-1183-8. |
[10] |
V. Muñoz and R. Pérez Marco, Ergodic solenoids and generalized currents, Rev. Mat. Complut., 24 (2011), 493-525.
doi: 10.1007/s13163-010-0050-7. |
[11] |
E. Paolini and E. Stepanov, Decomposition of acyclic normal currents in a metric space, J. Funct. Anal., 263 (2012), 3358-3390.
doi: 10.1016/j.jfa.2012.08.009. |
[12] |
E. Paolini and E. Stepanov, Structure of metric cycles and normal one-dimensional currents, J. Funct. Anal., 264 (2013), 1269-1295.
doi: 10.1016/j.jfa.2012.12.007. |
[13] |
S. Schwartzman, Asymptotic cycles, Ann. of Math. (2), 66 (1957), 270-284.
doi: 10.2307/1969999. |
[14] |
S. Schwartzman, Asymptotic cycles on non-compact spaces, Bull. London Math. Soc., 29 (1997), 350-352.
doi: 10.1112/S0024609396002561. |
[15] |
S. K. Smirnov, Decomposition of solenoidal vector charges into elementary solenoids and the structure of normal one-dimensional flows, St. Petersburg Math. J., 5 (1994), 841-867. |
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