Let be a two dimensional totally real submanifold of class in . A continuous map of the closed unit disk into that is holomorphic on the open disk and maps its boundary into is called an analytic disk with boundary in . Given an initial immersed analytic disk with boundary in , we describe the existence and behavior of analytic disks near with boundaries in small perturbations of in terms of the homology class of the closed curve in . We also prove a regularity theorem for immersed families of analytic disks, consider several examples, and construct a totally real three torus in with a bizzare polynomially convex hull.
Soit une sous-variété totalement réelle de dimension 2 et classe dans . Une application continue de disque-unité fermé dans , qui est holomorphe sur et applique sa frontière dans , est appelée un disque analytique avec frontière dans . Etant donné un disque initial avec frontière dans , on détermine l’existence des disques près de avec les frontières dans les petites perturbations de à l’aide de la classe d’homologie de courbe dans . On démontre aussi un théorème de régularité pour des familles des disques et on construit un tore totalement réel de dimension 3 dans avec une étrange enveloppe convexe polynomiale.
@article{AIF_1987__37_1_1_0, author = {Forstneric, Franc}, title = {Analytic disks with boundaries in a maximal real submanifold of ${\bf C}^2$}, journal = {Annales de l'Institut Fourier}, pages = {1--44}, publisher = {Institut Fourier}, address = {Grenoble}, volume = {37}, number = {1}, year = {1987}, doi = {10.5802/aif.1076}, mrnumber = {88j:32019}, zbl = {0583.32038}, language = {en}, url = {http://www.numdam.org/articles/10.5802/aif.1076/} }
TY - JOUR AU - Forstneric, Franc TI - Analytic disks with boundaries in a maximal real submanifold of ${\bf C}^2$ JO - Annales de l'Institut Fourier PY - 1987 SP - 1 EP - 44 VL - 37 IS - 1 PB - Institut Fourier PP - Grenoble UR - http://www.numdam.org/articles/10.5802/aif.1076/ DO - 10.5802/aif.1076 LA - en ID - AIF_1987__37_1_1_0 ER -
%0 Journal Article %A Forstneric, Franc %T Analytic disks with boundaries in a maximal real submanifold of ${\bf C}^2$ %J Annales de l'Institut Fourier %D 1987 %P 1-44 %V 37 %N 1 %I Institut Fourier %C Grenoble %U http://www.numdam.org/articles/10.5802/aif.1076/ %R 10.5802/aif.1076 %G en %F AIF_1987__37_1_1_0
Forstneric, Franc. Analytic disks with boundaries in a maximal real submanifold of ${\bf C}^2$. Annales de l'Institut Fourier, Volume 37 (1987) no. 1, pp. 1-44. doi : 10.5802/aif.1076. http://www.numdam.org/articles/10.5802/aif.1076/
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