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 2020 · math.DGShow all

4 papers · 2 filters

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…

math.DG2020★ 8 cited

Conjectures and Open Questions on the Structure and Regularity of Spaces with Lower Ricci Curvature Bounds

Aaron Naber

In this short note we review some known results on the structure and regularity of spaces with lower Ricci curvature bounds. We present some known and new open questions about next…

math.DG2020★ 4 cited

$d_{p}$ convergence and $ε$ -regularity theorems for entropy and scalar curvature lower bounds

Man-Chun Lee, Aaron Naber, Robin Neumayer

Consider a sequence of Riemannian manifolds $(M_{i}^{n}, g_{i})$ with scalar curvatures and entropies bounded below by small constants $R_{i}, μ_{i} \geq - ε_{i}$ . The goal of this paper is to und…

math.DG2020

Differential Harnack Inequalities on Path Space

Robert Haslhofer, Eva Kopfer, Aaron Naber

Recall that if $(M^{n}, g)$ satisfies $Ric \geq 0$ , then the Li-Yau Differential Harnack Inequality tells us for each nonnegative $f : M \to R^{+}$ , with $f_{t}$ its heat fl…

Boundary regularity and stability for spaces with Ricci bounded below

Conjectures and Open Questions on the Structure and Regularity of Spaces with Lower Ricci Curvature Bounds

dp​ convergence and ε-regularity theorems for entropy and scalar curvature lower bounds

Differential Harnack Inequalities on Path Space

$d_{p}$ convergence and $ε$ -regularity theorems for entropy and scalar curvature lower bounds