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In this paper we construct smooth Riemannian metrics on the sphere whichadmit smooth Zoll families of minimal hypersurfaces. This generalizes a theoremof Guillemin for the case of geodesics. The proof uses the Nash-Moser InverseFunction Theorem in the tame maps setting of Hamilton. This answers a questionof Yau on perturbations of minimal hypersurfaces in positive Ricci curvature.We also consider the case of the projective space and characterize thosemetrics on the sphere with minimal equators.

Riemannian metrics on the sphere with Zoll families of minimal hypersurfaces