Soit un ouvert relativement compact et localement pseudo-convexe de la variété analytique .
Alors,
1) Si le fibré tangent est positif, est -convexe.
2) Si admet une fonction strictement plurisousharmonique, est de Stein.
3) Si est l’espace total d’un morphisme de Stein à base de Stein, est de Stein.
Let be a relatively compact and locally pseudo-convex open subset of the analytic manifold .
We prove the following:
1) If the tangent bundle is positive, then is -convex.
2) If there exists on a strictly plurisubharmonic function, then is Stein.
3) If is the total space of a Stein morphism with Stein basis, then is Stein.
@article{AIF_1975__25_2_295_0, author = {Elencwajg, Georges}, title = {Pseudo-convexit\'e locale dans les vari\'et\'es kahl\'eriennes}, journal = {Annales de l'Institut Fourier}, pages = {295--314}, publisher = {Institut Fourier}, address = {Grenoble}, volume = {25}, number = {2}, year = {1975}, doi = {10.5802/aif.568}, mrnumber = {52 #8501}, zbl = {0278.32015}, language = {fr}, url = {http://archive.numdam.org/articles/10.5802/aif.568/} }
TY - JOUR AU - Elencwajg, Georges TI - Pseudo-convexité locale dans les variétés kahlériennes JO - Annales de l'Institut Fourier PY - 1975 SP - 295 EP - 314 VL - 25 IS - 2 PB - Institut Fourier PP - Grenoble UR - http://archive.numdam.org/articles/10.5802/aif.568/ DO - 10.5802/aif.568 LA - fr ID - AIF_1975__25_2_295_0 ER -
Elencwajg, Georges. Pseudo-convexité locale dans les variétés kahlériennes. Annales de l'Institut Fourier, Tome 25 (1975) no. 2, pp. 295-314. doi : 10.5802/aif.568. http://archive.numdam.org/articles/10.5802/aif.568/
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