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 $Y\cong M\#Z$ such that the Weyl energy of $g_Y$ is strictly smaller than the sum of Weyl energies of $g_M$ and $g_Z$.
Weyl energy and connected sums of four-manifolds
Andrea Malchiodi;Francesco Malizia
2025
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 $Y\cong M\#Z$ such that the Weyl energy of $g_Y$ is strictly smaller than the sum of Weyl energies of $g_M$ and $g_Z$.File in questo prodotto:
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