Cohomogeneity Two Ricci Solitons with Sub-Euclidean Volume
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12220_2025_Article_2232.pdf
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Author(s)
Firester, Benjy
Tsiamis, Raphael
Date Issued
October 27, 2025
Journal
The Journal of Geometric Analysis
Publisher
Springer US
Citation
Firester, B., Tsiamis, R. Cohomogeneity Two Ricci Solitons with Sub-Euclidean Volume. J Geom Anal 35, 407 (2025).
Version
Final published version
Abstract
We introduce new families of four-dimensional Ricci solitons of cohomogeneity two with volume collapsing ends. In a local presentation of the metric conformal to a product, we reduce the soliton equation to a degenerate Monge-Ampère equation for the conformal factor coupled with ODEs. We obtain explicit complete expanding solitons as well as abstract existence results for shrinking and steady solitons with boundary. These families of Ricci solitons specialize to classical examples of Einstein and soliton metrics. We also classify local solutions of this Monge-Ampère equation to prove rigidity for these solitons.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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Creative Commons Attribution
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DOI of Published Version
https://doi.org/10.1007/s12220-025-02232-9
