Abstract
We discuss the conformal boundary of a warped product of two length spaces and provide a method to calculate this in terms of the individual conformal boundaries. This technique is then applied to produce CAT(0)-spaces with complicated conformal boundaries. Finally, we prove that the conformal boundary of an Hadamard n-manifold is always simply connected for n >= 3, thus providing a bound for the level of complication of the boundary of such a manifold.
Original language | English |
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Journal | Journal of Geometric Analysis |
Volume | 18 |
Issue number | 3 |
Pages (from-to) | 704-719 |
ISSN | 1050-6926 |
DOIs | |
Publication status | Published - 2008 |
Keywords
- length space
- fundamental group
- ideal boundary
- warped product
- conformal boundary
- CAT(0)-space