[Les cônes tangents des courants positifs de De Rham]
Nous démontrons un resultat dʼunicité du cône tangent à un courant positif de De Rham aux points de densité strictement positive non isolés dans une varieté presque complexe quelconque.
We show a uniqueness result for tangent cones to positive- De Rham currents at non-isolated points of positive density in an arbitrary almost complex manifold.
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@article{CRMATH_2011__349_19-20_1025_0,
author = {Costante Bellettini},
title = {Tangent cones to positive-$ (1,1)$ {De} {Rham} currents},
journal = {Comptes Rendus. Math\'ematique},
pages = {1025--1029},
publisher = {Elsevier},
volume = {349},
number = {19-20},
year = {2011},
doi = {10.1016/j.crma.2011.08.023},
language = {en},
}
Costante Bellettini. Tangent cones to positive-$ (1,1)$ De Rham currents. Comptes Rendus. Mathématique, Volume 349 (2011) no. 19-20, pp. 1025-1029. doi : 10.1016/j.crma.2011.08.023. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2011.08.023/
[1] Tangent cones to positive- De Rham currents, 2011 | arXiv
[2] Sur le cône tangent à un courant positif fermé, J. Math. Pures Appl. (9), Volume 72 (1993) no. 6, pp. 517-536
[3] Sur lʼexistence du cône tangent à un courant positif fermé, Ark. Mat., Volume 28 (1990) no. 2, pp. 231-248
[4] Nombres de Lelong généralisés, théorèmes dʼintégralité et dʼanalyticité, Acta Math., Volume 159 (1987) no. 3–4, pp. 153-169
[5] Nuovi teoremi relativi alle misure -dimensionali in uno spazio ad r dimensioni, Ric. Mat., Volume 4 (1955), pp. 95-113 (in Italian)
[6] Gauge theory in higher dimensions, The Geometric Universe, Oxford Univ. Press, 1998, pp. 31-47
[7] Geometric Measure Theory, Grundl. Math. Wissenschaft., Band 153, Springer-Verlag, New York, 1969 (pp. xiv+676)
[8] Cartesian Currents in the Calculus of Variations I, Ergeb. Math. Grenzgeb. (3), vol. 37, Springer-Verlag, Berlin, 1998 (pp. xxiv+711)
[9] Calibrated geometries, Acta Math., Volume 148 (1982), pp. 47-157
[10] Plurisubharmonic functions and potential theory in several complex variables, Development of Mathematics 1950–2000, Birkhäuser, Basel, 2000, pp. 655-714
[11] Tangents of plurisubharmonic functions, Beijing, 1988, Springer, Berlin (1988), pp. 157-167
[12] Densité des fonctions plurisousharmoniques, Bull. Soc. Math. France, Volume 107 (1979) no. 3, pp. 295-304
[13] Fonctions plurisousharmoniques et formes différentielles positives, Gordon & Breach, Paris, 1968 (pp. ix+79)
[14] Sur la structure des courants positifs fermés, Séminaire Pierre Lelong (Analyse) (année 1975/76), Lecture Notes in Math., vol. 578, Springer, Berlin, 1977, pp. 136-156
[15] Dʼune variable à plusieurs variables en analyse complexe: les fonctions plurisousharmoniques et la positivité (1942–1962), Rev. Histoire Math., Volume 1 (1995) no. 1, pp. 139-157
[16] Uniqueness of tangent cones for semi-calibrated 2-cycles, Duke Math. J., Volume 152 (2010) no. 3, pp. 441-480
[17] The singular set of J-holomorphic maps into projective algebraic varieties, J. Reine Angew. Math., Volume 570 (2004), pp. 47-87
[18] A regularity theory for harmonic maps, J. Differential Geom., Volume 17 (1982) no. 1, pp. 307-335
[19] Analyticity of sets associated to Lelong numbers and the extension of closed positive currents, Invent. Math., Volume 27 (1974), pp. 53-156
[20] Gauge theory and calibrated geometry. I, Ann. of Math. (2), Volume 151 (2000) no. 1, pp. 193-268
[21] Elliptic Yang–Mills equation, Proc. Natl. Acad. Sci. USA, Volume 99 (2002) no. 24, pp. 15281-15286
[22] Tangent cones to two-dimensional area-minimizing integral currents are unique, Duke Math. J., Volume 50 (1983) no. 1, pp. 143-160
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