11 citations · 42 across the 14 of their papers we have counts for
19 papers
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…
A geometric take on Kostant's Convexity Theorem
Ricardo A. E. Mendes
Given a compact Lie group and an orthogonal -representation , we give a purely metric criterion for a closed subset of the orbit space to have convex pre-image in $…
Geography of pinched four-manifolds
Renato G. Bettiol, Mario Kummer, Ricardo A. E. Mendes
We prove several new restrictions on the Euler characteristic and signature of oriented 4-manifolds with (positively or negatively) pinched sectional curvature. In particular, we s…
Maximality of Laplacian Algebras, with Applications to Invariant Theory
Ricardo A. E. Mendes, Marco Radeschi
We show Laplacian algebras are maximal, and give applications to the Classical Invariant Theory of real orthogonal representations of compact groups, including: The solution of the…
Lifting isometries of orbit spaces
Ricardo A. E. Mendes
Given an orthogonal representation of a compact group, we show that any element of the connected component of the isometry group of the orbit space lifts to an equivariant isometry…
Laplacian algebras, manifold submetries and the Inverse Invariant Theory Problem
Ricardo A. E. Mendes, Marco Radeschi
Manifold submetries of the round sphere are a class of partitions of the round sphere that generalizes both singular Riemannian foliations, and the orbit decompositions by the orth…