16 citations · 32 across the 17 of their papers we have counts for
18 papers · 1 filter
Almgren frequency and Agmon convexity on rotationally symmetric Cartan-Hadamard manifolds
Luca F. Di Cerbo
We introduce a \emph{global} frequency function for harmonic functions on rotationally symmetric Cartan-Hadamard manifolds. In real hyperbolic space, we also identify a different f…
Aspherical Complex Surfaces, the Singer Conjecture, and Gromov-Lück Inequality
Michael Albanese, Luca F. Di Cerbo, Luigi Lombardi
We discuss the Singer conjecture and Gromov-Lück inequality for aspherical complex surfaces. We give a proof of the Singer conjecture for aspherical complex surface wit…
The signature of geometrically decomposable aspherical 4-manifolds
Luca Fabrizio Di Cerbo, Marco Golla
We construct examples of geometrically decomposable aspherical 4-manifolds with non-zero signature. We show that all such 4-manifolds satisfy the inequality (of Bogomolov--Miyaoka-…
Aspherical 4-Manifolds, Complex Structures, and Einstein Metrics
Michael Albanese, Luca F. Di Cerbo
We show that extended graph 4-manifolds with positive Euler characteristic cannot support a complex structure. This result stems from a new proof of the fact that a closed real-hyp…
Singer Conjecture for Varieties with Semismall Albanese Map and Residually Finite Fundamental Group
Luca F. Di Cerbo, Luigi Lombardi
We prove the Singer conjecture for varieties with semismall Albanese map and residually finite fundamental group.
On the impossibility of four-dimensional complex-hyperbolic Einstein Dehn filling
Luca F. Di Cerbo, Marco Golla
We show that the complex-hyperbolic Einstein Dehn filling compactification cannot possibly be performed in dimension four.
Generalized Graph Manifolds, Residual Finiteness, and the Singer Conjecture
Luca F. Di Cerbo, Michael Hull
We prove the Singer conjecture for extended graph manifolds and pure complex-hyperbolic higher graph manifolds with residually finite fundamental groups. In real dimension three, w…
On the Betti Numbers of Finite Volume Hyperbolic Manifolds
Luca F. Di Cerbo, Mark Stern
We obtain strong upper bounds for the Betti numbers of compact complex-hyperbolic manifolds. We use the unitary holonomy to improve the results given by the most direct application…
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…
Price Inequalities and Betti Number Growth on Manifolds without Conjugate Points
Luca F. Di Cerbo, Mark Stern
We derive Price inequalities for harmonic forms on manifolds without conjugate points and with a negative Ricci upper bound. The techniques employed in the proof work particularly…
A sharp cusp count for complex hyperbolic surfaces and related results
Gabriele Di Cerbo, Luca Fabrizio Di Cerbo
We derive a sharp cusp count for finite volume complex hyperbolic surfaces which admit smooth toroidal compactifications. We use this result, and the techniques developed in [DiC12…
Effective results for complex hyperbolic manifolds
Gabriele Di Cerbo, Luca F. Di Cerbo
The goal of this paper is to study the geometry of cusped complex hyperbolic manifolds through their compactifications. We characterize toroidal compactifications with non-nef cano…
Positivity in Kähler-Einstein theory
Gabriele Di Cerbo, Luca F. Di Cerbo
Tian initiated the study of incomplete Kähler-Einstein metrics on quasi-projective varieties with cone-edge type singularities along a divisor, described by the cone-angle $2π(1-α)…
On Kähler-Einstein surfaces with edge singularities
Luca Fabrizio Di Cerbo
In this paper we characterize logarithmic surfaces which admit Kähler-Einstein metrics with negative scalar curvature and small edge singularities along a normal crossing divisor.
Seiberg-Witten equations on surfaces of logarithmic general type
Luca Di Cerbo
We study the Seiberg-Witten equations on surfaces of logarithmic general type. First, we show how to construct irreducible solutions of the Seiberg-Witten equations for any metric…
Finite volume complex-hyperbolic surfaces, their toroidal compactifications, and geometric applications
Luca Fabrizio Di Cerbo
We study the classification of smooth toroidal compactifications of nonuniform ball quotients in the sense of Kodaira and Enriques. Moreover, several results concerning the Riemann…
Generic Properties of Homogeneous Ricci Solitons
Luca Fabrizio Di Cerbo
We discuss the geometry of homogeneous Ricci solitons. After showing the nonexistence of compact homogeneous and noncompact steady homogeneous solitons, we concentrate on the study…
A remark on Ricci Breathers and Solitons
Luca Fabrizio Di Cerbo
In this article we give a brief survey of breather and soliton solutions to the Ricci flow and prove a no breather and soliton theorem for homogeneous solutions.