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Integral of Scalar Curvature under Volume Collapse
We construct a smooth complete metric on $\R^3$ with strictly positive Ricci curvature and $\displaystyle \lim_{s\rightarrow\infty}s^{-1}\int_{B_p(s)}\Sc\ddμ= \infty$. This gives a negative answer to Shing-Tung Yau's question on the asymptotic scalar-curvature integral. We also give counterexamples
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