Calculus of Variations and Geometric Measure Theory

B. Firester - R. Tsiamis

Cohomogeneity two Ricci solitons with sub-Euclidean volume

created by tsiamis on 20 Jan 2026
modified by firester on 27 Jan 2026

[BibTeX]

Published Paper

Inserted: 20 jan 2026
Last Updated: 27 jan 2026

Journal: Journal of Geometric Analysis
Volume: 35
Number: 405
Year: 2024

ArXiv: 2408.13982 PDF
Links: Journal link

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.