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We construct examples of spherical space forms $(S^3/\Gamma,g)$ with positivescalar curvature and containing no stable embedded minimal surfaces, such thatthe following happens along the Ricci flow starting at $(S^3/\Gamma,g)$: astable embedded minimal two-sphere appears and a non-trivial singularityoccurs. We also give in dimension $3$ a general contruction of Type Ineckpinching and clarify the relationship between stable spheres andnon-trivial Type I singularities of the Ricci flow. Some symmetry assumptionsprevent the appearance of stable spheres, and this has consequences on thetypes of singularities which can occur for metrics with these symmetries.

Appearance of stable minimal spheres along the Ricci flow in positive scalar curvature