Integral Ricci curvatures volume comparison and fundamental groups of compact Riemannian manifolds (Q2480614)

Following \textit{P. Petersen} and \textit{G. Wei} [Geom. Funct. Anal. 7, 1031--1045 (1997; Zbl 0910.53029)], the author finds under integral curvature bounds a relative volume comparison estimate for the universal covering space of a compact Riemannian manifold \(M\). This estimate is then used to prove the results of \textit{M. Anderson} [J. Differ. Geom. 31, 265--275 (1990; Zbl 0696.53029)] and \textit{J.-G. Yun} [Arch. Math. 85, 167--174 (2005; Zbl 1083.53037)] for \(\pi_1(M)\) which were obtained under pointwise curvature bounds.