On asymptotic behavior of the mass of rays

Shioya, Takashi

doi:10.1090/S0002-9939-1990-0986652-X

On asymptotic behavior of the mass of rays

Author: Takashi Shioya
Journal: Proc. Amer. Math. Soc. 108 (1990), 495-505
MSC: Primary 53C20
DOI: https://doi.org/10.1090/S0002-9939-1990-0986652-X
MathSciNet review: 986652
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Abstract: We consider the measure of the set of all unit vectors tangent to rays emanating from a point in a finitely connected complete open Riemannian -manifold . If with one end admits total curvature , then this measure tends to $\min \{ 2\pi \chi (M) - c(M),2\pi \}$ as tends to infinity, where $\chi (M)$ is the Euler characteristic.

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