Yang, Deane \(L^ p\) pinching and compactness theorems for compact Riemannian manifolds. (English) Zbl 0753.53027 Forum Math. 4, No. 3, 323-333 (1992). It is studied how integral bounds on the curvature of a compact Riemannian manifold determine the topology. More precisely \(L^ p\)- bounds for the curvature with \(p>\dim(M)/2\) and a lower bound for the isoperimetric constant are assumed. The proof uses Hamilton’s Ricci flow and a global version of the Moser iteration. There are related results due to M. T. Anderson [Invent. Math. 102, No. 2, 429-445 (1990; Zbl 0711.53038)], L. Z. Gao [J. Differ. Geom. 32, No. 2, 349-381 (1990; Zbl 0752.53022); ibid., No. 1, 155-183 (1990; Zbl 0719.53024); ibid., No. 3, 713-774 (1990; Zbl 0721.53039)] and M. Min-Oo and E. Ruh [Comment. Math. Helv. 65, No. 1, 36-51 (1990; Zbl 0704.53031)]. Reviewer: H.-B.Rademacher (Bonn) Cited in 1 ReviewCited in 7 Documents MSC: 53C20 Global Riemannian geometry, including pinching Keywords:isoperimetric constant; Hamilton’s Ricci flow; Moser iteration Citations:Zbl 0752.53022; Zbl 0711.53038; Zbl 0719.53024; Zbl 0721.53039; Zbl 0704.53031 PDFBibTeX XMLCite \textit{D. Yang}, Forum Math. 4, No. 3, 323--333 (1992; Zbl 0753.53027) Full Text: DOI EuDML