Zobrazeno 1 - 10
of 113
pro vyhledávání: '"Bettiol, Renato G."'
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 description, i.e., can be described by an equivariant linear matrix i
Externí odkaz:
http://arxiv.org/abs/2408.03231
Autor:
Bettiol, Renato G., Piccione, Paolo
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 bifurcate from the 2-torus orbit of largest volume at a dense set of eccent
Externí odkaz:
http://arxiv.org/abs/2309.13758
Publikováno v:
J. Differential Equations 389 (2024), 285-304
We prove nonuniqueness results for complete metrics with constant positive fractional curvature conformal to the round metric on $S^n \setminus S^k$, using bifurcation techniques. These are singular (positive) solutions to a non-local equation with c
Externí odkaz:
http://arxiv.org/abs/2302.11073
We determine linear inequalities on the eigenvalues of curvature operators that imply vanishing of the twisted $\hat A$ genus on a closed Riemannian spin manifold, where the twisting bundle is any prescribed parallel bundle of tensors. These inequali
Externí odkaz:
http://arxiv.org/abs/2212.07548
Autor:
Bettiol, Renato G., Lauret, Emilio A.
Publikováno v:
Mat. Contemp. 57 (2023), 23-31
We show that spheres in all dimensions $\geq3$ can be deformed to have diameter larger than the distance between any pair of antipodal points. This answers a question of Yurii Nikonorov.
Comment: Mat. Contemp., to appear
Comment: Mat. Contemp., to appear
Externí odkaz:
http://arxiv.org/abs/2205.05186
Publikováno v:
Selecta Math. (N.S.) 30 (2024), no. 1, Paper No. 7, 29 pp
Following Gromov, a Riemannian manifold is called area-extremal if any modification that increases scalar curvature must decrease the area of some tangent 2-plane. We prove that large classes of compact 4-manifolds, with or without boundary, with non
Externí odkaz:
http://arxiv.org/abs/2205.00543
Publikováno v:
In Advances in Mathematics December 2024 458 Part B
Publikováno v:
Calc. Var. Partial Differential Equations 62 (2023), no. 1, Paper No. 13
We find examples of cohomogeneity one metrics on $S^4$ and $\mathbb C P^2$ with positive sectional curvature that lose this property when evolved via Ricci flow. These metrics are arbitrarily small perturbations of Grove--Ziller metrics with flat pla
Externí odkaz:
http://arxiv.org/abs/2112.13291
Autor:
Bettiol, Renato G., Piccione, Paolo
We use global bifurcation techniques to establish the existence of arbitrarily many geometrically distinct nonplanar embedded smooth minimal 2-spheres in sufficiently elongated 3-dimensional ellipsoids of revolution. More precisely, we quantify the g
Externí odkaz:
http://arxiv.org/abs/2111.14995
Autor:
Bettiol, Renato G., Piccione, Paolo
Publikováno v:
S\~ao Paulo J. Math. Sci. 16 (2022), no. 1, 486-507
We briefly survey global bifurcation techniques, and illustrate their use by finding multiple positive periodic solutions to a class of second order quasilinear ODEs related to the Yamabe problem. As an application, we give a bifurcation-theoretic pr
Externí odkaz:
http://arxiv.org/abs/2107.08181