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

43 papers

math.AP2024

Rectifiable Reifenberg and uniform positivity under almost calibrations

Nicholas Edelen, Aaron Naber, Daniele Valtorta

The Reifenberg theorem \cite{reif_orig} tells us that if a set $S \subseteq B_{2} \subseteq R^{n}$ is uniformly close on all points and scales to a $k$ -dimensional subspace, then…

math.AP2024★ 1 cited

Energy Identity for Stationary Harmonic Maps

Aaron Naber, Daniele Valtorta

In this paper we consider sequences $u_{j} : B_{2} \subseteq M \to N$ of stationary harmonic maps between smooth Riemannian manifolds with uniformly bounded energy $E[u_j]\equiv \int |\nab…

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…