Mathematical Analysis/Geometry
Tangent cones to positive-(1,1) De Rham currents
Comptes Rendus. Mathématique, Volume 349 (2011) no. 19-20, pp. 1025-1029.

We show a uniqueness result for tangent cones to positive-(1,1) De Rham currents at non-isolated points of positive density in an arbitrary almost complex manifold.

Nous démontrons un resultat dʼunicité du cône tangent à un courant positif (1,1) de De Rham aux points de densité strictement positive non isolés dans une varieté presque complexe quelconque.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2011.08.023
Bellettini, Costante 1

1 ETH Zürich, D-Math Rämistrasse 101, CH-8092 Zürich, Switzerland
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Bellettini, Costante. 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. http://www.numdam.org/articles/10.1016/j.crma.2011.08.023/

[1] Bellettini, C. Tangent cones to positive-(1,1) De Rham currents, 2011 | arXiv

[2] Blel, M. Sur le cône tangent à un courant positif fermé, J. Math. Pures Appl. (9), Volume 72 (1993) no. 6, pp. 517-536

[3] Blel, M.; Demailly, J.-P.; Mouzali, M. Sur lʼexistence du cône tangent à un courant positif fermé, Ark. Mat., Volume 28 (1990) no. 2, pp. 231-248

[4] Demailly, J.-P. Nombres de Lelong généralisés, théorèmes dʼintégralité et dʼanalyticité, Acta Math., Volume 159 (1987) no. 3–4, pp. 153-169

[5] De Giorgi, E. Nuovi teoremi relativi alle misure (r1)-dimensionali in uno spazio ad r dimensioni, Ric. Mat., Volume 4 (1955), pp. 95-113 (in Italian)

[6] Donaldson, S.K.; Thomas, R.P. Gauge theory in higher dimensions, The Geometric Universe, Oxford Univ. Press, 1998, pp. 31-47

[7] Federer, H. Geometric Measure Theory, Grundl. Math. Wissenschaft., Band 153, Springer-Verlag, New York, 1969 (pp. xiv+676)

[8] Giaquinta, M.; Modica, G.; Souček, J. Cartesian Currents in the Calculus of Variations I, Ergeb. Math. Grenzgeb. (3), vol. 37, Springer-Verlag, Berlin, 1998 (pp. xxiv+711)

[9] Harvey, R.; Lawson, H.B. Jr. Calibrated geometries, Acta Math., Volume 148 (1982), pp. 47-157

[10] Kiselman, C.O. Plurisubharmonic functions and potential theory in several complex variables, Development of Mathematics 1950–2000, Birkhäuser, Basel, 2000, pp. 655-714

[11] Kiselman, C.O. Tangents of plurisubharmonic functions, Beijing, 1988, Springer, Berlin (1988), pp. 157-167

[12] Kiselman, C.O. Densité des fonctions plurisousharmoniques, Bull. Soc. Math. France, Volume 107 (1979) no. 3, pp. 295-304

[13] Lelong, P. Fonctions plurisousharmoniques et formes différentielles positives, Gordon & Breach, Paris, 1968 (pp. ix+79)

[14] Lelong, P. 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] Lelong, P. 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] Pumberger, D.; Rivière, T. Uniqueness of tangent cones for semi-calibrated 2-cycles, Duke Math. J., Volume 152 (2010) no. 3, pp. 441-480

[17] Rivière, T.; Tian, G. The singular set of J-holomorphic maps into projective algebraic varieties, J. Reine Angew. Math., Volume 570 (2004), pp. 47-87

[18] Schoen, R.; Uhlenbeck, K. A regularity theory for harmonic maps, J. Differential Geom., Volume 17 (1982) no. 1, pp. 307-335

[19] Siu, Y.-T. Analyticity of sets associated to Lelong numbers and the extension of closed positive currents, Invent. Math., Volume 27 (1974), pp. 53-156

[20] Tian, G. Gauge theory and calibrated geometry. I, Ann. of Math. (2), Volume 151 (2000) no. 1, pp. 193-268

[21] Tian, G. Elliptic Yang–Mills equation, Proc. Natl. Acad. Sci. USA, Volume 99 (2002) no. 24, pp. 15281-15286

[22] White, B. 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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