A NOTE ON THE UNCLOUDING THE SKY OF NEGATIVELY CURVED MANIFOLDS
2008 ◽
Vol 77
(3)
◽
pp. 413-424
Keyword(s):
AbstractThe problem of finding geodesics that avoid certain obstacles in negatively curved manifolds has been studied in different situations. In this note we give a generalization of the unclouding theorem of J. Parkkonen and F. Paulin: there is a constant s0=1.534 such that for any Hadamard manifold M with curvature ≤−1 and for any family of disjoint balls or horoballs {Ca}a∈A and for any point p∈M−⋃ a∈ACa if we shrink these balls uniformly by s0 one can always find a geodesic ray emanating from p that avoids the shrunk balls. It will be shown that in the theorem above one can replace the balls by arbitrary convex sets.
1993 ◽
Vol 118
(1)
◽
pp. 205-205
Keyword(s):
2021 ◽
Vol 0
(0)
◽
Keyword(s):
2005 ◽
Vol 9
(3)
◽
pp. 401-406
◽
2009 ◽
Vol 29
(4)
◽
pp. 1141-1161
2004 ◽
Vol 24
(3)
◽
pp. 803-824
◽
Keyword(s):