A. Naber

activity

20062024

most citedStructure Theory of Metric-Measure Spaces with Lower Ricci Curvature Bounds

96 citations · 554 across the 37 of their papers we have counts for

collaborators

Showing math.DGShow all

36 papers · 1 filter

math.DG2023

Six dimensional counterexample to the Milnor Conjecture

Elia Bruè, Aaron Naber, Daniele Semola

We extend our previous work by building a smooth complete manifold $(M^{6}, g, p)$ with $Ric \geq 0$ and whose fundamental group $π_{1} (M^{6}) = Q / Z$ is infinitely…

math.DG2023★ 4 cited

Lower Ricci Curvature and Nonexistence of Manifold Structure

Erik Hupp, Aaron Naber, Kai-Hsiang Wang

It is known that a limit $(M_{j}^{n}, g_{j}) \to (X^{k}, d)$ of manifolds $M_{j}$ with uniform lower bounds on Ricci curvature must be $k$ -rectifiable for some unique $\dim X:= k\leq n = \dim M…

math.DG2023★ 2 cited

Stability of Tori under Lower Sectional Curvature

Elia Brue, Aaron Naber, Daniele Semola

Let $(M_{i}^{n}, g_{i}) \to (X, d_{X})$ be a Gromov-Hausdorff converging sequence of Riemannian manifolds with $Sec_{g_{i}} \geq - 1$ , $diam (M_{i}) \leq D$ , and such that the $M_{i}^{n}$ …

math.DG2023★ 3 cited

Fundamental Groups and the Milnor Conjecture

Elia Bruè, Aaron Naber, Daniele Semola

It was conjectured by Milnor in 1968 that the fundamental group of a complete manifold with nonnegative Ricci curvature is finitely generated. The main result of this paper is a co…

math.DG2021

Codimension four regularity of generalized Einstein structures

Xin Fu, Aaron Naber, Jeffrey Streets

We establish codimension 4 regularity of noncollapsed sequences of metrics with bounds on natural generalizations of the Ricci tensor. We obtain a priori L2 curvature estimates on…

math.DG2020★ 2 cited

Boundary regularity and stability for spaces with Ricci bounded below

Elia Bruè, Aaron Naber, Daniele Semola

This paper studies the structure and stability of boundaries in noncollapsed $RCD (K, N)$ spaces, that is, metric-measure spaces $(X, d, H^{N})$ with lower Ricc…