Geodesic
On a metric property of analytic sets
Izvestiya. Mathematics, Tome 10 (1976) no. 6, pp. 1333-1338 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

Let $H$ be an algebraic set in $\mathbf C^n$ containing the origin and let $S=\{z\in\mathbf C^n:|z|=1\}$ be the unit sphere. Conjecture. The diameter of one of the connected components of $H\cap S$ is greater than one. In this article it is shown that this is false if the requirement that $H$ be algebraic is weakened to the demand that the projections onto the coordinate planes be open. If, however, $S$ is replaced by the boundary of the unit polydisc, then the conjecture holds and the proof uses only the openness of the projection. Bibliography: 3 titles. 
@article{IM2_1976_10_6_a7,
     author = {V. K. Beloshapka},
     title = {On a~metric property of analytic sets},
     journal = {Izvestiya. Mathematics},
     pages = {1333--1338},
     year = {1976},
     volume = {10},
     number = {6},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1976_10_6_a7/}
}
TY  - JOUR
AU  - V. K. Beloshapka
TI  - On a metric property of analytic sets
JO  - Izvestiya. Mathematics
PY  - 1976
SP  - 1333
EP  - 1338
VL  - 10
IS  - 6
UR  - http://geodesic.mathdoc.fr/item/IM2_1976_10_6_a7/
LA  - en
ID  - IM2_1976_10_6_a7
ER  - 
%0 Journal Article
%A V. K. Beloshapka
%T On a metric property of analytic sets
%J Izvestiya. Mathematics
%D 1976
%P 1333-1338
%V 10
%N 6
%U http://geodesic.mathdoc.fr/item/IM2_1976_10_6_a7/
%G en
%F IM2_1976_10_6_a7
V. K. Beloshapka. On a metric property of analytic sets. Izvestiya. Mathematics, Tome 10 (1976) no. 6, pp. 1333-1338. http://geodesic.mathdoc.fr/item/IM2_1976_10_6_a7/

[1] Ronkin L. I., Vvedenie v teoriyu tselykh funktsii mnogikh peremennykh, «Nauka», M., 1971 | MR | Zbl

[2] Lelong P., “Proprietés métriques des variétés analytiques complexes définies par une équation”, Ann. Scient. Ecole Supér, 67 (1950), 393–419 | MR | Zbl

[3] Springer Dzh., Vvedenie v teoriyu rimanovykh poverkhnostei, IL, M., 1960