Sbornik. Mathematics, Tome 79 (1994) no. 2, pp. 459-469
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R. Ts. Musaelyan. The existence of infinite polygons in a two-dimensional metric of variable negative curvature. Sbornik. Mathematics, Tome 79 (1994) no. 2, pp. 459-469. http://geodesic.mathdoc.fr/item/SM_1994_79_2_a12/
@article{SM_1994_79_2_a12,
author = {R. Ts. Musaelyan},
title = {The existence of infinite polygons in a~two-dimensional metric of variable negative curvature},
journal = {Sbornik. Mathematics},
pages = {459--469},
year = {1994},
volume = {79},
number = {2},
language = {en},
url = {http://geodesic.mathdoc.fr/item/SM_1994_79_2_a12/}
}
TY - JOUR
AU - R. Ts. Musaelyan
TI - The existence of infinite polygons in a two-dimensional metric of variable negative curvature
JO - Sbornik. Mathematics
PY - 1994
SP - 459
EP - 469
VL - 79
IS - 2
UR - http://geodesic.mathdoc.fr/item/SM_1994_79_2_a12/
LA - en
ID - SM_1994_79_2_a12
ER -
%0 Journal Article
%A R. Ts. Musaelyan
%T The existence of infinite polygons in a two-dimensional metric of variable negative curvature
%J Sbornik. Mathematics
%D 1994
%P 459-469
%V 79
%N 2
%U http://geodesic.mathdoc.fr/item/SM_1994_79_2_a12/
%G en
%F SM_1994_79_2_a12
We prove the existence of certain classes of convex noncompact domains on two-dimensional manifolds of variable negative Gaussian curvature. These domains are defined as the intersection of finitely or countably many half-planes (a half-plane is one of the two parts of the whole manifold bounded by a geodesic) whose boundaries have no common points. The boundary of such convex noncompact domains consists of complete geodesics. In this paper, these domains are called infinite polygons (IP for short). There exist IPs in the Lobachevsky plane.
