Weyl energy and connected sums of four-manifolds

Andrea Malchiodi; Francesco Malizia

paper

Weyl energy and connected sums of four-manifolds

arXiv:2505.17752

Abstract

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 there exists a metric $g_{Y}$ on the connected sum $Y ≅ M # Z$ such that the Weyl energy of $g_{Y}$ is strictly smaller than the sum of Weyl energies of $g_{M}$ and $g_{Z}$ .

40 pages. Comments are welcome!