6 problems

Let $(M,g)$ be a compact Riemannian manifold without boundary, and call it a C-manifold if all of its geodesics are closed. Call $(M,g)$ Zoll if all of its closed geodesics have th…

A Zoll metric on $S^2$ is a Riemannian metric whose geodesics are all simple closed curves of equal length. A marked Zoll structure is a Zoll structure together with a choice of an…

A Zoll metric on a smooth manifold is a Riemannian metric whose geodesics are all simple closed curves of equal length. On $\mathbb R\mathbb P^2$, the standard metric is the consta…

Conjectural equivalence. The following conditions are equivalent:

On a Zoll manifold, the square roots of the Laplace eigenvalues form clusters concentrating along an arithmetic progression, with the width of the $k^{th}$ cluster on the order of…

A Zoll manifold is a Riemannian manifold on which every geodesic is closed. A point is a blow-down point if all geodesic directions through it loop back; thus every point is a blow…