4 papers
On the Rational Hyperbolicity problem
Ricardo Mendes, Alessandro Minuzzo, Marco Radeschi
We prove that a compact simply connected manifold with a variationally complete -action satisfying certain mild conditions (e.g. trivial principal isotropy, or simply connec…
Manifold submetries from compact homogeneous spaces
Samuel Lin, Ricardo A. E. Mendes, Marco Radeschi
We show that singular Riemannian foliations, or, more generally, manifold submetries, defined on a compact normal homogeneous space, have algebraic nature. Moreover, in this case t…
Two results on the Convex Algebraic Geometry of sets with continuous symmetries
Renato G. Bettiol, Mario Kummer, Ricardo A. E. Mendes
We prove two results on convex subsets of Euclidean spaces invariant under an orthogonal group action. First, we show that invariant spectrahedra admit an equivariant spectrahedral…
Diameter and focal radius of submanifolds
Ricardo A. E. Mendes
In this note, we give a characterization of immersed submanifolds of simply-connected space forms for which the quotient of the extrinsic diameter by the focal radius achieves the…