Geodesic
Asymptotic behavior of volume of convex sets in Adamar manifold
Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 6 (1999), pp. 223-233.

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We estimate the limit at infinity of the quotients volume/area for a family of convex with respect to horospheres sets expanding over the whole simply connected complete Riemannian manifold of nonpositive sectional curvature. A similar result is obtained for $\lambda$-convex sets in Hyperbolic space. 
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     author = {A. A. Borisenko and D. I. Vlasenko},
     title = {Asymptotic behavior of volume of convex sets in {Adamar} manifold},
     journal = {\v{Z}urnal matemati\v{c}eskoj fiziki, analiza, geometrii},
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     volume = {6},
     year = {1999},
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     url = {http://geodesic.mathdoc.fr/item/JMAG_1999_6_a2/}
}
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A. A. Borisenko; D. I. Vlasenko. Asymptotic behavior of volume of convex sets in Adamar manifold. Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 6 (1999), pp. 223-233. http://geodesic.mathdoc.fr/item/JMAG_1999_6_a2/