Metrics of constant scalar curvatures conformal to a Riemannian product with a round sphere (2008)
We consider the conformal class of the Riemannian product $g_0 + g$, where $g_0$ is the constant curvature metric on $S^m$ and $g$ is a metric of constant scalar curvature on some closed manifold. We...
Gabriel P. Paternain, Jimmy Petean
Abstract. Let (M n, g) be a closed Riemannian manifold and let Kmax be any positive upper bound for the sectional curvature. We prove that
Isoperimetric regions in spherical cones and Yamabe constants of $M\times S^1$ (2007)
Given closed Riemannian manifold $(M^n, g)$ of positive Ricci curvature $Ricci(g) \geq (n-1)g$ we study isoperimetric regions on the spherical cone over $M$. When $g$ is Einstein we use this to...
On Yamabe constants of Riemannian products (2006)
Akutagawa, Kazuo, Florit, Luis A., Petean, Jimmy
For a closed Riemannian manifold $(M^m,g)$ of constant positive scalar curvature and any other closed Riemannian manifold $(N^n,h)$, we show that the limit of the Yamabe constants of the Riemannian...
Ricci curvature and Yamabe constants (2005)
We prove that if a closed unit volume Riemannian manifold, $(M^n, g)$, has Ricci curvature bounded from below by r>0 then the Yamabe constant of the conformal class of $g$ is at least $n.r$. This...
Collapsing manifolds obtained by Kummer-type constructions (2005)
Paternain, Gabriel P., Petean, Jimmy
We construct F-structures on a Bott manifold and on some other manifolds obtained by Kummer-type constructions. We also prove that if M=E#X, where E is a fiber bundle with structure group G and a...
Zero entropy and bounded topology (2004)
Paternain, Gabriel P., Petean, Jimmy
We study the existence of Riemannian metrics with zero topological entropy on a closed manifold M with infinite fundamental group. We show that such a metric does not exist if there is a finite...
On the growth rate of contractible closed geodesics on reducible manifolds (2003)
Paternain, Gabriel, Petean, Jimmy
We prove exponential growth rate of contractible closed geodesics for an arbitrary bumpy metric on manifolds of the form X#Y, where the fundamental group of X has a subgroup of finite index at least...
Entropy and collapsing of compact complex surfaces (2003)
Paternain, Gabriel P., Petean, Jimmy
We study the problem of existence of F-structures on compact complex surfaces, giving a complete classification modulo the gap in the classification of surfaces of class VII. We then use these...
Minimal entropy and collapsing with curvature bounded from below (2000)
Paternain, Gabriel, Petean, Jimmy
We show that if a closed manifold M admits an F-structure (possibly of rank 0) then its minimal entropy vanishes. In particular, this is the case if M admits a non-trivial circle action. As a...
Einstein manifolds of non-negative sectional curvature and entropy (2000)
Paternain, Gabriel, Petean, Jimmy
We find obstructions to the existence of Einstein metrics of non-negative sectional curvature on a smooth closed simply connected manifold of any dimension. The results are achieved by combining the...
The Yamabe invariant of simply connected manifolds (1998)
We prove that the Yamabe invariant of any simply connected smooth manifold of dimension n greater than four is non-negative. Equivalently that the infimum of the L^{n/2} norm of the scalar curvature,...
Surgery and the Yamabe invariant (1998)
We study the Yamabe invariant of manifolds obtained as connected sums along submanifolds of codimension greater than 2. In particular, given a compact smooth manifold M which does not admit metrics...
Computations of the Yamabe invariant (1998)
For a compact connected manifold M of dimension n greater than 3 and with no metric of positive scalar curvature, we prove that the Yamabe invariant is unchanged under surgery on spheres of dimension...
Indefinite Kähler-Einstein metrics on compact complex surfaces /--by Jimmy Petean. (1997)
Thesis (Ph. D.)--State University of New York at Stony Brook, 1997.
Indefinite Kaehler-Einstein metrics on Compact Complex Surfaces (1996)
Indefinite Kaehler solutions of the Einstein equations are studied, and it is almost completely determined which compact complex surfaces admit such metrics.