6 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…
Bifurcations of Clifford tori in ellipsoids
Renato G. Bettiol, Paolo Piccione
We prove that 3-dimensional ellipsoids invariant under a 2-torus action contain infinitely many distinct immersed minimal tori, with at most one exception. These minimal tori bifur…
Nonplanar minimal spheres in ellipsoids of revolution
Renato G. Bettiol, Paolo Piccione
We use global bifurcation techniques to establish the existence of arbitrarily many geometrically distinct nonplanar embedded smooth minimal 2-spheres in sufficiently elongated 3-d…
Curvature operators and rational cobordism
Renato G. Bettiol, McFeely Jackson Goodman
We determine linear inequalities on the eigenvalues of curvature operators that imply vanishing of the twisted genus on a closed Riemannian spin manifold, where the twisti…
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…
Counting Homogeneous Einstein Metrics
Renato G. Bettiol, Hannah Friedman
We present an explicit upper bound on the number of isolated homogeneous Einstein metrics on compact homogeneous spaces whose isotropy representations consist of pairwise inequival…