15 papers · 1 filter
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…
Positive curvature and rational ellipticity in cohomogeneity three
Elahe Khalili Samani, Marco Radeschi
We prove that a closed, simply connected, positively curved, cohomogeneity-three manifold whose quotient space has no boundary is rationally elliptic, thus providing a generalizati…
Isoparametric foliations and bounded geometry
Manuel Krannich, Alexander Lytchak, Marco Radeschi
We prove that there are only finitely many isoparametrically foliated closed connected Riemannian manifolds with bounded geometry, fixed dimension , and finite fundamental…
A Weyl's Law for Singular Riemannian Foliations with Applications to Invariant Theory
Samuel Lin, Ricardo A. E. Mendes, Marco Radeschi
We prove a version of Weyl's Law for the basic spectrum of a closed singular Riemannian foliation with basic mean curvature. In the special case of $M=\mathbb{S}^…
Rational ellipticity of -manifolds from their quotients
Elahe Khalili Samani, Marco Radeschi
We prove that if a compact, simply connected Riemannian -manifold has orbit space isometric to some other quotient with having zero topological entropy, then…