G. Antonelli

activity

20192026

most citedAsymptotic isoperimetry on non collapsed spaces with lower Ricci bounds

32 citations · 130 across the 34 of their papers we have counts for

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18 papers · 1 filter

math.DG2026

Removability of non-isolated singularities for Einstein metrics and RCD spaces

Gioacchino Antonelli, Gábor Székelyhidi

In this paper we establish removable singularities results for Einstein metrics and for metrics with Ricci curvature bounded below. Let $n \geq 2$ . On a closed $n$ -manifold, we show…

math.DG2026

Universal Volume Growth Bounds from Positive Intermediate Curvature

Gioacchino Antonelli

Let $n, m$ be integers such that $n \geq 2$ and $0 \leq m \leq n - 2$ . Let $C_{m + 1}$ denote the $(m + 1)$ -intermediate curvature introduced by Brendle--Hirsch--Johne. We prove that there ar…

math.DG2026

Spaces of metrics with positive spectral scalar curvature

Gioacchino Antonelli, Georg Frenck, Bernhard Hanke

Let $n \geq 2$ and let $M^{n}$ be a closed connected smooth manifold. Let $R^{γ} (M)$ be the space of smooth Riemannian metrics $g$ on $M$ for which the generalized conformal Laplace oper…

math.DG2026

Rigidity and flexibility under spectral Ricci lower bounds and mean-convex boundary

Gioacchino Antonelli, Yangyang Li, Paul Sweeney

We study Riemannian manifolds $(M^{n}, g)$ with mean-convex boundary whose Ricci curvature is nonnegative in a spectral sense. Our first main result is a sharp spectral extension of a…

math.DG2025

Isoperimetric problems and lower bounds on curvature

Gioacchino Antonelli

This note surveys some classical results and recent developments on the interplay between lower curvature bounds and the isoperimetric problem. It is based on mini-courses given at…

math.DG2025

Connected sum of manifolds with spectral Ricci lower bounds

Gioacchino Antonelli, Kai Xu

Let $n > 2$ , $γ > \frac{n - 1}{n - 2}$ , and $λ \in R$ . We prove that if $M$ and $N$ are two smooth $n$ -manifolds that admit a complete Riemannian metric satisfying \[-γΔ+ \mathr…