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A Counterexample to Yau's Conjectured Asymptotic Scalar-Curvature Integral Bound
Abstract
A complete one-ended three-manifold with strictly positive Ricci curvature is constructed such that limsupR→∞1/R∫B(p,R) Scal dV=+∞. 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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BibTeX
@misc{hao2026counterexample,
title = {{A Counterexample to Yau's Conjectured Asymptotic Scalar-Curvature Integral Bound}},
author = {Tianze Hao and Jintian Zhu},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.06533},
eprint = {2609.06533},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.06533},
}
RIS
TY - UNPB
TI - A Counterexample to Yau's Conjectured Asymptotic Scalar-Curvature Integral Bound
AU - Tianze Hao
AU - Jintian Zhu
PY - 2026
DA - 2026/09/06
PB - arXiv
DO - 10.48550/arxiv.2609.06533
UR - https://arxiv.org/abs/2609.06533
AB - A complete one-ended three-manifold with strictly positive Ricci curvature is constructed such that limsup_R→∞1/R∫_B(p,R) Scal dV=+∞. 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.
ER -