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We prove that given a 3-manifold with an arbitrary metric   $(M^3, g)$   of positive Ricci curvature, there exists a sweepout of   $M$   by surfaces of genus   $\leq 3$   and areas bounded by   $C vol(M^3, g)^{2/3}$  . We use this result to construct a sweepout of   $M$   by 1-cycles of length at most   $C vol(M^3, g)^{1/3}$  , giving a partial answer to a question of L. Guth.

Sweeping Out 3-Manifold of Positive Ricci Curvature by Short 1-Cycles Via Estimates of Min–Max Surfaces