Let Mn be a compact, simply connected n (≥3)-dimensional Riemannian manifold without bound-ary and Sn be the unit sphere Euclidean space Rn+1. We derive a differentiable sphere theorem whenever themanifold concerned satisfies that the sectional curvature KM is not larger than 1, while Ric(M)≥n+2 4 and the volume V (M) is not larger than (1 + η)V (Sn) for some positive number η depending only on n.
WANG PeiHe1 & WEN YuLiang2 1School of Mathematical Sciences, Qufu Normal University, Qufu 273165, China
In this note, we discuss the monotonicity of the first eigenvalue of the p-Laplace operator （p ≥2） along the Ricci flow on closed Riemannian manifolds. We prove that the first eigenvalue of the p-Laplace operator is nondecreasing along the Ricci flow under some different curvature assumptions, and therefore extend some parts of Ma＇s results [Ann. Glob. Anal.Geom,29,287-292（2006）]
