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Unique asymptotics of steady Ricci solitons with symmetry

  • Zilu Ma

    University of Tennessee, Knoxville, USA

  • Hamidreza Mahmoudian

    Arizona State University, Tempe, USA

    • Nataša Šešum

      Rutgers University, Piscataway, USA
    Unique asymptotics of steady Ricci solitons with symmetry cover

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    Abstract

    We study 4d gradient steady Ricci solitons which are weak -solutions and exhibit -symmetry. Under a weak curvature decay condition, we find precise geometric asymptotics of such solitons, which are similar to those for 3d compact -solutions found in [Comm. Pure Appl. Math. 75, 1032–1073 (2022)]. This is the first step towards the classification of 4d gradient steady Ricci solitons and more general ancient Ricci flows.

    Cite this article

    Zilu Ma, Hamidreza Mahmoudian, Nataša Šešum, Unique asymptotics of steady Ricci solitons with symmetry. J. Eur. Math. Soc. (2026), published online first

    DOI 10.4171/JEMS/1774