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arXiv · 2610.29882

A variational construction for Einstein metrics on connected sums of $S^2\times S^2$

Adrian Chun-Pong Chu·Daniel Stern
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Abstract

For each positive integer $n$, we give a variational construction of a positive Einstein metric on the connected sum of $n$ copies of $S^2\times S^2$, with coupled toric and dihedral symmetries. More precisely, we obtain these metrics via a min-max construction for the total scalar curvature, which is in some sense dual to the usual max-min formulation of the smooth Yamabe invariant within this symmetry class, with more favorable analytic properties.

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Adrian Chun-Pong Chu, Daniel Stern. 2026-10-21. A variational construction for Einstein metrics on connected sums of $S^2\times S^2$. https://arxiv.org/abs/2610.29882

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