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…