F. Bei

activity

20112026

most citedGeneral perversities and L^2 de Rham and Hodge theorems for stratified pseudomanifolds

4 citations · 14 across the 17 of their papers we have counts for

collaborators

18 papers

math.DG2026

Geometric Rigidity via Almost-Harmonic Twisted Spinors

Francesco Bei, Simone Cecchini

We establish sharp scalar-curvature bounds and rigidity consequences of Gromov's exact-lift two-form method. Let $(M^{n}, g)$ , $n \geq 4$ even, be a closed spin Riemannian manifold car…

math.DG2023

Compact convergence, deformation of the $L^{2}$ - $\partial$ -complex and canonical $K$ -homology classes

Francesco Bei

Let $(X, γ)$ be a compact, irreducible Hermitian complex space of complex dimension $m$ and with $dim (sing (X)) = 0$ . Let $(F, τ) \to X$ be a Hermitian holomorp…

math.CV2022

Weakly Kähler hyperbolic manifolds and the Green--Griffiths--Lang conjecture

Francesco Bei, Simone Diverio, Philippe Eyssidieux +1

We introduce the notion of weakly Kähler hyperbolic manifold which generalizes that of Kähler hyperbolic manifold given in the early '90s by M. Gromov, and establish its basic feat…

math.DG2020

A note on higher Todd genera of complex manifolds

Francesco Bei, Paolo Piazza

Let $M$ be a compact complex manifold. In this paper we give a simple proof of the bimeromorphic invariance of the higher Todd genera of $M$ , a result first proved implicitly by Br…

math.DG2019★ 1 cited

Degenerating Hermitian metrics, canonical bundle and spectral convergence

Francesco Bei

Let $(M, J)$ be a compact complex manifold of complex dimension $m$ and let $g_{s}$ be a one-parameter family of Hermitian forms on $M$ that are smooth and positive definite for each…

math.DG2019★ 2 cited

On analytic Todd classes of singular varieties

Francesco Bei, Paolo Piazza

Let $(X, h)$ be a compact and irreducible Hermitian complex space. This paper is devoted to various questions concerning the analytic K-homology of $(X, h)$ . In the fist part, assumi…

math.DG2018

Symplectic manifolds, $L^{p}$ -cohomology and $q$ -parabolicity

Francesco Bei

Let $(M, ω, J, g)$ be a non-compact almost Kähler manifold. In this paper we provide various criteria that assure that $ω^{k}$ induces a non trivial class in the reduced $L^{p}$ maximal/m…

math.DG2017

Von Neumann dimension, Hodge index theorem and geometric applications

Francesco Bei

This note contains a reformulation of the Hodge index theorem within the framework of Atiyah's $L^{2}$ -index theory. More precisely, given a compact Kähler manifold $(M, h)$ of even c…

math.FA2017★ 1 cited

Kac regular sets and Sobolev spaces in geometry, probability and quantum physics

Francesco Bei, Batu Güneysu

Let $Ω \subset M$ be an open subset of a Riemannian manifold $M$ and let $V:M\to \IR$ be a Kato decomposable potential. With $W_{0}^{1, 2} (M; V)$ the natural form domain of the Schröd…

math.DG2017★ 3 cited

On the Laplace-Beltrami operator on compact complex spaces

Francesco Bei

Let $(X, h)$ be a compact and irreducible Hermitian complex space of complex dimension $v > 1$ . In this paper we show that the Friedrichs extension of both the Laplace-Beltrami operat…

math.DG2016★ 1 cited

Degenerating Hermitian metrics and spectral geometry of the canonical bundle

Francesco Bei

Let $(X, h)$ be a compact and irreducible Hermitian complex space of complex dimension $m$ . In this paper we are interested in the Dolbeault operator acting on the space of $L^{2}$ se…

math.DG2015

On the space of connections having non-trivial twisted harmonic spinors

Francesco Bei, Nils Waterstraat

We consider Dirac operators on odd-dimensional compact spin manifolds which are twisted by a product bundle. We show that the space of connections on the twisting bundle which yiel…

math.PR2015

q-parabolicity of stratified pseudomanifolds and other singular spaces

Franceso Bei, Batu Güneysu

The main result of this paper is a sufficient condition in order to have a compact Thom-Mather stratified pseudomanifold endowed with a $c^$ -iterated edge metric on its regula…

math.DG2015★ 1 cited

Sobolev spaces and Bochner Laplacian on complex projective varieties and stratified pseudomanifolds

Francesco Bei

Let $V \subset C P^{n}$ be an irreducible complex projective variety of complex dimension $v$ and let $g$ be the Kähler metric on $\reg(V)$, the regular part of $V$ ,…

math.DG2014

Scattering theory of the Hodge-Laplacian under a conformal perturbation

Francesco Bei, Batu Güneysu, Jörn Müller

Let $g$ and $g ~$ be Riemannian metrics on a noncompact manifold $M$ , which are conformally equivalent. We show that under a very mild \emph{first order} control on the confo…

math.DG2014

On the $L^{2} -$ Poincaré duality for incomplete riemannian manifolds: a general construction with applications

Francesco Bei

Let $(M, g)$ be an open, oriented and incomplete riemannian manifold of dimension $m$ . Under some general conditions we show that it is possible to build a Hilbert complex $(L^2Ω^i(…

math.DG2012★ 1 cited

Poincaré duality, Hilbert complexes and geometric applications

Francesco Bei

Let $(M, g)$ an open and oriented riemannian manifold. The aim of this paper is to study some properties of the two following sequences of $L^{2}$ cohomology groups: $H^i_{2,m\rightar…

math.DG2011★ 4 cited

General perversities and L^2 de Rham and Hodge theorems for stratified pseudomanifolds

Francesco Bei

Given a compact stratified pseudomanifold with a Thom-Mather stratification and a class of riemannian metrics over its regular part, we study the relationships between the $L^{2}$ …

Geometric Rigidity via Almost-Harmonic Twisted Spinors

Compact convergence, deformation of the L2-∂-complex and canonical K-homology classes

Weakly Kähler hyperbolic manifolds and the Green--Griffiths--Lang conjecture

A note on higher Todd genera of complex manifolds

Degenerating Hermitian metrics, canonical bundle and spectral convergence

On analytic Todd classes of singular varieties

Symplectic manifolds, Lp-cohomology and q-parabolicity

Von Neumann dimension, Hodge index theorem and geometric applications

Kac regular sets and Sobolev spaces in geometry, probability and quantum physics

On the Laplace-Beltrami operator on compact complex spaces

Degenerating Hermitian metrics and spectral geometry of the canonical bundle

On the space of connections having non-trivial twisted harmonic spinors

q-parabolicity of stratified pseudomanifolds and other singular spaces

Sobolev spaces and Bochner Laplacian on complex projective varieties and stratified pseudomanifolds

Scattering theory of the Hodge-Laplacian under a conformal perturbation

On the L2−Poincaré duality for incomplete riemannian manifolds: a general construction with applications

Poincaré duality, Hilbert complexes and geometric applications

General perversities and L^2 de Rham and Hodge theorems for stratified pseudomanifolds

Compact convergence, deformation of the $L^{2}$ - $\partial$ -complex and canonical $K$ -homology classes

Symplectic manifolds, $L^{p}$ -cohomology and $q$ -parabolicity

On the $L^{2} -$ Poincaré duality for incomplete riemannian manifolds: a general construction with applications