Juan Miguel Ruiz

activity

20082026

most citedMultipeak solutions for the Yamabe equation

2 citations · 3 across the 10 of their papers we have counts for

collaborators

12 papers

math.DG2026

On K-peak solutions for the Yamabe equation on product manifolds

Juan Miguel Ruiz, Areli Vázquez Juárez

Let $(M^{n}, g)$ and $(X^{m}, h)$ be closed manifolds $m, n > 2$ , such that $(X, h)$ has constant positive scalar curvature. We consider the one parameter family of products $(M\times X,…

math.DG2026

Isoperimetric estimates in the product of small and large volume manifolds

Juan Miguel Ruiz, Areli Vázquez Juárez

Let $(M^{m}, g)$ , $(N^{n}, h)$ be closed Riemannian manifolds, $m, n \geq 2$ , with concave isoperimetric profiles and volumes $V_{M}$ , $V_{N}$ respectively. We consider a one parameter family…

math.DG2023

Lower bounds for isoperimetric profiles and Yamabe constants

Juan Miguel Ruiz, Areli Vázquez Juárez

We estimate explicit lower bounds for the isoperimetric profiles of the Riemannian product of a compact manifold and the Euclidean space with the flat metric, $(M^m\times \mathbb{R…

math.DG2020

Isoperimetric estimates in low dimensional Riemannian products

Juan Miguel Ruiz, Areli Vazquez Juarez

Let $(T^{k}, h_{k}) = (S_{r_{1}}^{1} \times S_{r_{2}}^{1} \times ... \times S_{r_{k}}^{1}, d t_{1}^{2} + d t_{2}^{2} + ... + d t_{k}^{2})$ be flat tori, $r_{k} \geq ... \geq r_{2} \geq r_{1} > 0$ and $(R^{n}, g_{E})$ the Euclidea…

math.AP2018★ 2 cited

Multipeak solutions for the Yamabe equation

Carolina A. Rey, Juan Miguel Ruiz

Let $(M, g)$ be a closed Riemannian manifold of dimension $n \geq 3$ and $x_{0} \in M$ be an isolated local minimum of the scalar curvature $s_{g}$ of $g$ . For any positive integer $k$ w…

math.DG2016

Multiplicity of constant scalar curvature metrics on warped products

Juan Miguel Ruiz

Let $(M^{m}, g_{M})$ be a closed, connected manifold with positive scalar curvature and $(T^{k}, g)$ some flat $k$ -Torus of unit volume. By a result of F. Dobarro and E. Lami Dozo, there e…

math.DG2015

Stable solutions of the Yamabe equation on non-compact manifolds

Jimmy Petean, Juan Miguel Ruiz

We consider the Yamabe equation on a complete non-compact Riemannian manifold and study the condition of stability of solutions. If $(M^{m}, g)$ is a closed manifold of constant posit…

math.DG2014

Minimal hypersurfaces in R^n \times S^m

Jimmy Petean, Juan Miguel Ruiz

We classify minimal hypersurfaces in $R^{n} \times S^{m}$ , $n, m \geq 2$ , which are invariant by the canonical action of $O (n) \times O (m)$ . We also construct compact and noncompact exa…

math.DG2012★ 1 cited

On the Yamabe constants of $S^2 \times \re^3$ and $S^3 \times \re^2$

Jimmy Petean, Juan Miguel Ruiz

We compare the isoperimetric profiles of $S^2 \times \re^3$ and of $S^3 \times \re^2$ with that of a round 5-sphere (of appropriate radius). Then we use this comparison to obtain l…

math.DG2010

Isoperimetric profile comparisons and Yamabe constants

Jimmy Petean, Juan Miguel Ruiz

We estimate from below the isoperimetric profile of $S^2 \times \re^2$ and use this information to obtain lower bounds for the Yamabe constant of $S^2 \times \re^2$. This provides…

math.DG2009

Results on the existence of the Yamabe minimizer of M^m \times R^n

Juan Miguel Ruiz

We let (M^m, g) be a closed smooth Riemannian manifold (m >1) with positive scalar curvature S_g, and prove that the Yamabe constant of (M \times R^n,g+g_E) is achieved by a metric…

math.DG2008

On metrics of positive Ricci curvature conformal to MxR^m

Juan Miguel Ruiz

Let (M, g) be a closed Riemannian manifold and gE the Euclidean metric. We show that for m > 1, (M x R^m, (g + gE)) is not conformal to a positive Einstein manifold. Moreover, (M x…