Andrea Malchiodi

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20242026

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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.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.DG2024

Yamabe metrics on conical manifolds

Mattia Freguglia, Andrea Malchiodi

We prove existence of Yamabe metrics on singular manifolds with conical points and conical links of Einstein type that include orbifold structures. We deal with metrics of generic…