Local Volume Estimate for Manifolds with L 2 -bounded Curvature
نویسنده
چکیده
It is important to study asymptotic behavior of complete manifold without the assumption of pointwise Ricci curvature bound. A volume growth and curvature decay result was obtained in [4] for various classes of complete, noncompact, Bach-flat metrics in dimension 4. Some similar results were also claimed in [1]. In this note we consider a more general case, that is, the Bach tensor may not necessarily vanish. Since Bach tensor can be viewed as a second derivative of the Ricci tensor, there will be a priori no L bound for it, where p > 2. So we may consider the case that the L norm of the Bach tensor is finite. Our main result is to give a local volume estimate:
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