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arXiv · 2609.06533

A Counterexample to Yau's Conjectured Asymptotic Scalar-Curvature Integral Bound

Tianze Hao·Jintian Zhu
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Abstract

A complete one-ended three-manifold with strictly positive Ricci curvature is constructed such that $$ \limsup_{R\to\infty}\frac1R\int_{B(p,R)} Scal\,dV=+\infty. $$ The construction combines an explicit toric lens carrying a large scalar-curvature integral with a three-dimensional angular pair of pants and an adaptive sequence of hybrid blocks.

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Tianze Hao, Jintian Zhu. 2026-09-06. A Counterexample to Yau's Conjectured Asymptotic Scalar-Curvature Integral Bound. https://arxiv.org/abs/2609.06533

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