Francesco Malizia

activity

20242026

collaborators

6 papers

math.AP2026

Quantization for Palais-Smale sequences of the Liouville functional on closed surfaces

Andrea Malchiodi, Francesco Malizia, Luca Martinazzi

In this paper we prove a quantization property for Palais-Smale sequences of functionals related to Liouville equations on compact surfaces. While these equations have been extensi…

math.DG2026

Decreasing Weyl's energy by connected sums with locally conformally flat manifolds

Andrea Malchiodi, Francesco Malizia

We study the Weyl functional on connected sums of two four-dimensional manifolds $(M, g_{M})$ and $(Z, g_{Z})$ , assuming $g_{M}$ is Bach-flat and $g_{Z}$ locally conformally flat. We show th…

math.DG2025

Min-max theory and Yamabe metrics on conical four-manifolds

Mattia Freguglia, Andrea Malchiodi, Francesco Malizia

We prove existence of Yamabe metrics on four-manifolds possessing finitely-many conical points with $Z_{2}$ -group, using for the first time a min-max scheme in the singular…

math.AP2025

Simplicity and boundary behavior of spike sequences for a superlinear problem in plasma physics

Paolo Cosentino, Francesco Malizia

We prove that spike sequences related to a nonlinear problem of Grad-Shafranov type are always simple and always converge toward interior points of the domain. This sharpens the bl…

math.DG2025

Weyl energy and connected sums of four-manifolds

Andrea Malchiodi, Francesco Malizia

Given two closed, oriented Riemannian four-manifolds $(M, g_{M})$ and $(Z, g_{Z})$ , which are not locally conformally flat and not both self-dual or both anti-self-dual, we prove that th…

math.AP2024

Compactness of Palais-Smale sequences with controlled Morse Index for a Liouville type functional

Francesco Malizia

We prove that Palais-Smale sequences for Liouville type functionals on closed surfaces are precompact whenever they satisfy a bound on their Morse index. As a byproduct, we obtain…