Andrea Tamburelli

activity

20162026

most citedPlanar minimal surfaces with polynomial growth in the

Sp (4, R)

-symmetric space

7 citations · 26 across the 22 of their papers we have counts for

collaborators

28 papers

math.GT2026

Euler characteristic and flat cohomology of convex projective $4$ -manifolds

Andrea Tamburelli

Let $M = Ω/Γ$ be a closed properly convex real projective $4$ -manifold. We prove the Chern-Hopf-Thurston conjecture for this class of manifolds, i.e. $χ (M) \geq 0$ . The argument transf…

math.DG2026

Extending Donaldson's HyperKähler Structure via Minimal Surfaces into $PSL (2, C)$

Christian El Emam, Filippo Mazzoli, Nicholas Rungi +2

We construct a deformation space for minimal immersions into $PSL (2, C)$ with its holomorphic Killing form, and define an explicit, mapping class group invariant,…

math.GT2026

On Line-Hyperplane Structures for Hitchin Representations

Parker Evans, Andrea Tamburelli

Let $n \geq 4$ and $ρ : π_{1} S \to P S L (n, R)$ be a Hitchin representation. We study the topology of a cocompact domain of discontinuity $Ω_{ρ}$ in the flag manifold $\ma…

math.DG2026

Global comparison of pseudo-Kähler structures on the $SL (3, R)$ -Hitchin component

Andrea Tamburelli

We compare the closed $2$ -form $ω_{f}$ constructed by Rungi-Tamburelli and Goldman's symplectic form $ω_{G}$ on the $SL (3, R)$ -Hitchin component. In particular, we esta…

math.DG2025

Para-complex geometry and cyclic Higgs bundles

Nicholas Rungi, Andrea Tamburelli

We introduce para-complex and pseudo-Riemannian geometric methods for the study of representations of surface groups in $SL (2 m + 1, R)$ . For $m = 1$ our techniques all…

math.DG2024

Complex Lagrangian minimal surfaces, bi-complex Higgs bundles and $SL (3, C)$ -quasi-Fuchsian representations

Nicholas Rungi, Andrea Tamburelli

In this paper we introduce complex minimal Lagrangian surfaces in the bi-complex hyperbolic space and study their relation with representations in $SL (3, C)$ . Our…

math.DG2023

The moduli space of flat maximal space-like embeddings in pseudo-hyperbolic space

Nicholas Rungi, Andrea Tamburelli

We study the moduli space of flat maximal space-like embeddings in $H^{2, 2}$ from various aspects. We first describe the associated Codazzi tensors to the embedding in the…

math.DG2023

Pseudo-Kähler structure on the $SL (3, R)$ -Hitchin component and Goldman symplectic form

Nicholas Rungi, Andrea Tamburelli

The aim of this paper is to show the existence and give an explicit description of a pseudo-Riemannian metric and a symplectic form on the $SL (3, R)$ -Hitc…

math.SG2022

Global Darboux coordinates for complete Lagrangian fibrations and an application to the deformation space of $R P^{2}$ -structures in genus one

Nicholas Rungi, Andrea Tamburelli

In this paper we study a broad class of complete Hamiltonian integrable systems, namely the ones whose associated Lagrangian fibration is complete and has non compact fibres. By st…

math.DG2022

Limits of Cubic Differentials and Buildings

John Loftin, Andrea Tamburelli, Michael Wolf

In the Labourie-Loftin parametrization of the Hitchin component of surface group representations into SL(3,R), we prove an asymptotic formula for holonomy along rays in terms of lo…

math.DG2021

Pseudo-Kähler geometry of properly convex projective structures on the torus

Nicholas Rungi, Andrea Tamburelli

In this paper we prove the existence of a pseudo-Kähler structure on the deformation space $B_{0} (T^{2})$ of properly convex $R P^{2}$ -structures over the torus.…

math.GT2021★ 1 cited

A closed ball compactification of a maximal component via cores of trees

Giuseppe Martone, Charles Ouyang, Andrea Tamburelli

We show that, in the character variety of surface group representations into the Lie group $PSL (2, R) \times PSL (2, R)$ , the compactification of t…

math.DG2021★ 1 cited

Para-hyperKähler geometry of the deformation space of maximal globally hyperbolic anti-de Sitter three-manifolds

Filippo Mazzoli, Andrea Seppi, Andrea Tamburelli

In this paper we study the para-hyperKähler geometry of the deformation space of MGHC anti-de Sitter structures on $Σ \times R$ , for $Σ$ a closed oriented surface. We show th…

math.DG2021

Boundary of the Gothen components

Charles Ouyang, Andrea Tamburelli

In this short note we describe an interesting new phenomenon about the $Sp (4, R)$ -character variety. Precisely, we show that the Hitchin component and all Gothen c…

math.DG2020★ 1 cited

Length spectrum compactification of the $SO_{0} (2, 3)$ -Hitchin component

Charles Ouyang, Andrea Tamburelli

We find a compactification of the $SO_{0} (2, 3)$ -Hitchin component by studying the degeneration of the induced metric on the unique equivariant maximal surface in the 4-dim…

math.DG2020

Riemannian metrics on the moduli space of GHMC anti-de Sitter structures

Andrea Tamburelli

In this short note we explain how to adapt the construction of two Riemannian metrics on the $SL (3, R)$ -Hitchin component to the deformation space of globally hype…

math.DG2020★ 7 cited

Planar minimal surfaces with polynomial growth in the $Sp (4, R)$ -symmetric space

Andrea Tamburelli, Michael Wolf

We study the asymptotic geometry of a family of conformally planar minimal surfaces with polynomial growth in the $Sp (4, R)$ -symmetric space. We describe a homeomo…

math.DG2019★ 5 cited

Limits of Blaschke metrics

Charles Ouyang, Andrea Tamburelli

We find a compactification of the $SL (3, R)$ -Hitchin component by studying the degeneration of the Blaschke metrics on the associated equivariant affine spheres. I…

math.GT2019

Fenchel-Nielsen coordinates on the augmented moduli space of anti-de Sitter structures

Andrea Tamburelli

In this paper we combine our recent work on regular globally hyperbolic maximal anti-de Sitter structures with the classical theory of globally hyperbolic maximal Cauchy-compact an…

math.DG2019★ 5 cited

Wild globally hyperbolic maximal anti-de Sitter structures

Andrea Tamburelli

Let $Σ$ be a connected, oriented surface with punctures and negative Euler characteristic. We introduce wild globally hyperbolic anti-de Sitter structures on $Σ \times R$ a…

math.DG2018

Degeneration of globally hyperbolic maximal anti-de Sitter structures along pinching sequences

Andrea Tamburelli

Let $S$ be a closed oriented surface of genus at least $2$ . Using the parameterisation of the deformation space of globally hyperbolic maximal anti-de Sitter structures on $S \time…

math.DG2018★ 4 cited

Regular globally hyperbolic maximal anti-de Sitter structures

Andrea Tamburelli

Let $Σ$ be a connected, oriented surface with punctures and negative Euler characteristic. We introduce regular globally hyperbolic anti-de Sitter structures on $Σ\times \mathbb{R}…

math.DG2017

Polynomial quadratic differentials on the complex plane and light-like polygons in the Einstein Universe

Andrea Tamburelli

We construct geometrically a homeomorphism between the moduli space of polynomial quadratic differentials on the complex plane and light-like polygons in the 2-dimensional Einstein…

math.DG2017

Degeneration of globally hyperbolic maximal anti-de Sitter structures along rays

Andrea Tamburelli

Using the parameterisation of the deformation space of GHMC anti-de Sitter structures on $S \times R$ by the cotangent bundle of the Teichmüller space of $S$ , we study how…

Euler characteristic and flat cohomology of convex projective 4-manifolds

Extending Donaldson's HyperKähler Structure via Minimal Surfaces into PSL(2,C)

On Line-Hyperplane Structures for Hitchin Representations

Global comparison of pseudo-Kähler structures on the SL(3,R)-Hitchin component

Para-complex geometry and cyclic Higgs bundles

Complex Lagrangian minimal surfaces, bi-complex Higgs bundles and SL(3,C)-quasi-Fuchsian representations

The moduli space of flat maximal space-like embeddings in pseudo-hyperbolic space

Pseudo-Kähler structure on the SL(3,R)-Hitchin component and Goldman symplectic form

Global Darboux coordinates for complete Lagrangian fibrations and an application to the deformation space of RP2-structures in genus one

Limits of Cubic Differentials and Buildings

Pseudo-Kähler geometry of properly convex projective structures on the torus

A closed ball compactification of a maximal component via cores of trees

Para-hyperKähler geometry of the deformation space of maximal globally hyperbolic anti-de Sitter three-manifolds

Boundary of the Gothen components

Length spectrum compactification of the SO0​(2,3)-Hitchin component

Riemannian metrics on the moduli space of GHMC anti-de Sitter structures

Planar minimal surfaces with polynomial growth in the Sp(4,R)-symmetric space

Limits of Blaschke metrics

Fenchel-Nielsen coordinates on the augmented moduli space of anti-de Sitter structures

Wild globally hyperbolic maximal anti-de Sitter structures

Degeneration of globally hyperbolic maximal anti-de Sitter structures along pinching sequences

Regular globally hyperbolic maximal anti-de Sitter structures

Polynomial quadratic differentials on the complex plane and light-like polygons in the Einstein Universe

Degeneration of globally hyperbolic maximal anti-de Sitter structures along rays

Euler characteristic and flat cohomology of convex projective $4$ -manifolds

Extending Donaldson's HyperKähler Structure via Minimal Surfaces into $PSL (2, C)$

Global comparison of pseudo-Kähler structures on the $SL (3, R)$ -Hitchin component

Complex Lagrangian minimal surfaces, bi-complex Higgs bundles and $SL (3, C)$ -quasi-Fuchsian representations

Pseudo-Kähler structure on the $SL (3, R)$ -Hitchin component and Goldman symplectic form

Global Darboux coordinates for complete Lagrangian fibrations and an application to the deformation space of $R P^{2}$ -structures in genus one

Length spectrum compactification of the $SO_{0} (2, 3)$ -Hitchin component

Planar minimal surfaces with polynomial growth in the $Sp (4, R)$ -symmetric space