Alessandro Pigati

Lower Ricci curvature bounds and the orientability of spaces

Abstract We study orientability in spaces with Ricci curvature bounded below. Building on the theory developed by Honda, we establish equivalent characterizations of orientability for Ricci limit and RCD \mathrm{RCD} spaces in terms of the orientability of their manifold part. We...

Decay of excess for the abelian Higgs model

We prove that entire critical points (u,\nabla) of the self-dual U(1) -Yang–Mills–Higgs functional E_{1} , with energy E_{1}(u,\nabla;B_{R})\leq(1+\tau(n))\cdot2\pi\omega_{n-2}R^{n-2} for all R>0 , have unique blow-down. Moreover, we show that they are two-dimensional in ambient...