The Yamabe Invariant of $\mathbb{RP}^3$ via Harmonic Functions

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Liam Mazurowski , Xuan Yao This is my paper · ORCID

classification math.DGmath.GT

keywords functionsharmonicinvariantmathbbyamabebraygiveneves

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abstract

We use harmonic functions to give a new proof of a result of Bray and Neves on the Yamabe invariant of $\mathbb{RP}^3$

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Euclidean Domains with Nearly Maximal Yamabe Quotient
math.DG 2025-01 conditional novelty 7.0 of 10

A domain in R^3 whose Yamabe quotient is close to the maximal ball value is close to a ball: diffeomorphic, nearly round, and Gromov-Hausdorff close after scaling.