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- W2317159536 abstract "For a locally symmetric space M, we define a compactification M∪M(∞) which we call the “geodesic compactification”. It is constructed by adding limit points in M(∞) to certain geodesics in M. The geodesic compactification arises in other contexts. Two general constructions of Gromov for an ideal boundary of a Riemannian manifold give M(∞) for locally symmetric spaces. Moreover, M(∞) has a natural group theoretic construction using the Tits building. The geodesic compactification plays two fundamental roles in the harmonic analysis of the locally symmetric space:1) it is the minimal Martin compactification for negative eigenvalues of the Laplacian, and 2) it can be used to parameterize the eigenfunctions of the Laplacian in continuous spectrum on L 2 ." @default.
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- W2317159536 date "2002-01-01" @default.
- W2317159536 modified "2023-09-23" @default.
- W2317159536 title "Geometry of compactifications of locally symmetric spaces" @default.
- W2317159536 doi "https://doi.org/10.5802/aif.1893" @default.
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