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Annals of Global Analysis and Geometry

, Volume 26, Issue 3, pp 209–229 | Cite as

Surgery, Curvature, and Minimal Volume

  • Chanyoung Sung
Article

Abstract

On a Riemannian manifold X, we consider aK+s, where a is a nonnegative constant, K is the sectional curvature and s is the scalar curvature. It is shown that if X admits a metric with aK+s > 0, then so does any manifold obtained from X by surgeries of codimension ≥3. This implies the existence of such metrics on certain compact simply connected manifolds of dimension ≥5 by using the cobordism argument. We also study the corresponding minimal volume problem. As a corollary, we derive that every compact simply connected manifold of dimension ≥5 and every compact complex surface of Kodaira dimension ≤1 whose minimal model is not of Class VII collapse with aK+s bounded below.

surgery curvature minimal volume 

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© Kluwer Academic Publishers 2004

Authors and Affiliations

  • Chanyoung Sung

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