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A variational construction for Einstein metrics on connected sums of S2× S2

  • 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 S2× S2, 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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Cite

BibTeXRIS
BibTeX
@misc{chu2026variational,
  title = {{A variational construction for Einstein metrics on connected sums of $S^2\times S^2$}},
  author = {Adrian Chun-Pong Chu and Daniel Stern},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.29882},
  eprint = {2610.29882},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.29882},
}
RIS
TY  - UNPB
TI  - A variational construction for Einstein metrics on connected sums of S^2× S^2
AU  - Adrian Chun-Pong Chu
AU  - Daniel Stern
PY  - 2026
DA  - 2026/10/21
PB  - arXiv
DO  - 10.48550/arxiv.2610.29882
UR  - https://arxiv.org/abs/2610.29882
AB  - 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× 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.
ER  -