Jurgen Julio-Batalla

activity

20182026

collaborators

9 papers

math.DG2026

Zero modes on product Riemannian manifolds

Jurgen Julio-Batalla

This paper is concerned with the zero mode equation $D_{g} φ = i A \cdot φ$ on product of closed spin manifolds $(M_{1}^{n_{1}} \times M_{2}^{n_{2}}, g_{1} + g_{2}, σ)$ of dimensions $n_{1} \leq n_{2}$ respecti…

math.DG2026

Spinor inequality for magnetic fields on spin manifolds

Jurgen Julio-Batalla

This paper is concerned with the zero mode equation $D_{g} φ = i A \cdot φ$ on closed spin manifold $(M^{n}, g, σ)$ of positive scalar curvature. Here $A$ is a real one form on $M$ . We proved…

math.AP2024

Nodal solutions to Paneitz-type equations

Jurgen Julio-Batalla, Jimmy Petean

On a closed Riemannian manifold $(M^{n}, g)$ with a proper isoparametric function $f$ we consider the equation $Δ^{2} u - α Δ u + β u = u^{q}$ , where $α$ and $β$ are positive constants satisf…

math.DG2024

Spinorial Yamabe-type equations and the Bär-Hijazi-Lott invariant

Jurgen Julio-Batalla

We consider on a closed Riemannian spin manifold $(M^{n}, g, σ)$ the spinorial Yamabe type equation $D_{g} φ = λ ∣ φ ∣^{\frac{2}{n - 1}} φ$ , where $φ$ is a spinor field and $λ$ is a positive cons…

math.AP2024

A note on sign-changing solutions to supercritical Yamabe-type equations

Jurgen Julio-Batalla

On a closed Riemannian manifold $(M^{n}, g)$ , we consider the Yamabe-type equation $- Δ_{g} u + λ u = λ ∣ u ∣^{q - 1} u$ , where $λ \in R_{+}$ and $q > 1$ . We assume that $M$ admits a pro…

math.DG2023

Global bifurcation for Paneitz type equations and constant Q-curvature metrics

Jurgen Julio-Batalla, Jimmy Petean

We consider the Paneitz-type equation $Δ^{2} u - α Δ u + β (u - u^{q}) = 0$ on a closed Riemannian manifold $(M, g)$ . We reduce the equation to a fourth-order ordinary differential equation as…

math.DG2020

Nodal solutions of Yamabe-type equations on positive Ricci curvature manifolds

Jurgen Julio-Batalla, Jimmy Petean

We consider a closed cohomogeneity one Riemannian manifold $(M^{n}, g)$ of dimension $n \geq 3$ . If the Ricci curvature of $M$ is positive, we prove the existence of infinite nodal so…

math.DG2019

Global bifurcation techniques for Yamabe type equations on Riemannian manifolds

Alejandro Betancourt de la Parra, Jurgen Julio-Batalla, Jimmy Petean

We consider a closed Riemannian manifold $(M^{n}, g)$ of dimension $n \geq 3$ and study positive solutions of the equation $- Δ_{g} u + λ u = λ u^{q}$ , with $λ > 0$ , $q > 1$ . If $M$ supports a p…

math.DG2018

Isoparametric functions on $R^{n} \times M^{m}$

Jurgen Julio-Batalla

We classify the isoparametric functions on $R^{n} \times M^{m}$ , $n, m \geq 2$ , with compact level sets, where $M^{m}$ is a connected, closed Riemannian manifold o…

Zero modes on product Riemannian manifolds

Spinor inequality for magnetic fields on spin manifolds

Nodal solutions to Paneitz-type equations

Spinorial Yamabe-type equations and the Bär-Hijazi-Lott invariant

A note on sign-changing solutions to supercritical Yamabe-type equations

Global bifurcation for Paneitz type equations and constant Q-curvature metrics

Nodal solutions of Yamabe-type equations on positive Ricci curvature manifolds

Global bifurcation techniques for Yamabe type equations on Riemannian manifolds

Isoparametric functions on Rn×Mm

Isoparametric functions on $R^{n} \times M^{m}$