L. D. Di Cerbo

collaborators

3 papers

math.DG2025

Aspherical Complex Surfaces, the Singer Conjecture, and Gromov-LÃ¼ck Inequality $I ¨ \geq ∣ I ¨ ∣$

Michael Albanese, Luca F. Di Cerbo, Luigi Lombardi

We discuss the Singer conjecture and Gromov-LÃ¼ck inequality $I ¨ \geq ∣ I ¨ ∣$ for aspherical complex surfaces. We give a proof of the Singer conjecture for aspherical complex surface…

math.DG2025

A rigidity theorem for Einstein $4$ -manifolds with sectional curvature of a fixed sign, and its consequences

Luca F. Di Cerbo

Any oriented $4$ -dimensional Einstein metric with semi-definite sectional curvature satisfies the pointwise inequality \[ \frac{|s|}{\sqrt{6}}\geq|W^+|+|W^-|, \] where $s$ , $W^{+}$ a…

math.DG2024

Harmonic Forms, Price Inequalities, and Benjamini-Schramm Convergence

Luca F. Di Cerbo, Mark Stern

We study Betti numbers of sequences of Riemannian manifolds which Benjamini-Schramm converge to their universal covers. Using the Price inequalities we developed elsewhere, we deri…

Aspherical Complex Surfaces, the Singer Conjecture, and Gromov-LÃ¼ck Inequality I¨≥∣I¨∣

A rigidity theorem for Einstein 4-manifolds with sectional curvature of a fixed sign, and its consequences

Harmonic Forms, Price Inequalities, and Benjamini-Schramm Convergence

Aspherical Complex Surfaces, the Singer Conjecture, and Gromov-LÃ¼ck Inequality $I ¨ \geq ∣ I ¨ ∣$

A rigidity theorem for Einstein $4$ -manifolds with sectional curvature of a fixed sign, and its consequences