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arXiv · 2308.03184

New Counterexamples to Min-Oo's Conjecture via Tunnels

Paul Sweeney Jr
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Abstract

Min-Oo's Conjecture is a positive curvature version of the positive mass theorem. Brendle, Marques, and Neves produced a perturbative counterexample to this conjecture. In 2021, Carlotto asked if it is possible to develop a novel gluing method in the setting of Min-Oo's Conjecture and in doing so produce new counterexamples. Here we build upon the perturbative counterexamples of Brendle--Marques--Neves in order to construct counterexamples that make advances on the theme expressed in Carlotto's question. These new counterexamples are non-perturbative in nature; moreover, we also produce examples with more complicated topology. Our main tool is a quantitative version of Gromov--Lawson Schoen--Yau surgery.

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Paul Sweeney Jr. 2025-02-24. New Counterexamples to Min-Oo's Conjecture via Tunnels. https://arxiv.org/abs/2308.03184

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