7 problems

Let $M$ be an irreducible symmetric space of compact type and rank greater than one. A polar action on $M$ is an isometric group action admitting a section, namely a complete immer…

Palais–Terng conjecture. If $\mathcal H$ is integrable, then its integral manifolds can be extended to sections.

Equifocality conjecture. More generally, submanifolds with parallel focal structure in irreducible compact symmetric spaces of higher rank are equifocal, hence have codimension one…

Let a compact Lie group act smoothly and isometrically on a simply connected compact manifold of nonnegative curvature. The action is irreducible when its associated reflection gro…

Let $M$ be a simply connected polar manifold, meaning a Riemannian manifold with an isometric polar group action, and suppose that $M$ is hyperbolic in the sense that its section h…

A polar action is an isometric group action admitting a section, a submanifold meeting every orbit orthogonally. Let a compact simply connected manifold have nonnegative sectional…

Correspondence conjecture. It is conjectured that all polar actions on Hilbert spaces correspond to $P(G,H)$ actions under suitable assumptions on the cohomogeneity.