7 citations · 26 across the 22 of their papers we have counts for
22 papers · 1 filter
Extending Donaldson's HyperKähler Structure via Minimal Surfaces into
Christian El Emam, Filippo Mazzoli, Nicholas Rungi +2
We construct a deformation space for minimal immersions into with its holomorphic Killing form, and define an explicit, mapping class group invariant,…
Global comparison of pseudo-Kähler structures on the -Hitchin component
Andrea Tamburelli
We compare the closed -form constructed by Rungi-Tamburelli and Goldman's symplectic form on the -Hitchin component. In particular, we esta…
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 . For our techniques all…
Complex Lagrangian minimal surfaces, bi-complex Higgs bundles and -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 . Our…
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 from various aspects. We first describe the associated Codazzi tensors to the embedding in the…
Pseudo-Kähler structure on the -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 -Hitc…
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…
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 of properly convex -structures over the torus.…
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 , for a closed oriented surface. We show th…
Boundary of the Gothen components
Charles Ouyang, Andrea Tamburelli
In this short note we describe an interesting new phenomenon about the -character variety. Precisely, we show that the Hitchin component and all Gothen c…
Length spectrum compactification of the -Hitchin component
Charles Ouyang, Andrea Tamburelli
We find a compactification of the -Hitchin component by studying the degeneration of the induced metric on the unique equivariant maximal surface in the 4-dim…
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 -Hitchin component to the deformation space of globally hype…
Planar minimal surfaces with polynomial growth in the -symmetric space
Andrea Tamburelli, Michael Wolf
We study the asymptotic geometry of a family of conformally planar minimal surfaces with polynomial growth in the -symmetric space. We describe a homeomo…
Limits of Blaschke metrics
Charles Ouyang, Andrea Tamburelli
We find a compactification of the -Hitchin component by studying the degeneration of the Blaschke metrics on the associated equivariant affine spheres. I…
Wild globally hyperbolic maximal anti-de Sitter structures
Andrea Tamburelli
Let be a connected, oriented surface with punctures and negative Euler characteristic. We introduce wild globally hyperbolic anti-de Sitter structures on a…
Degeneration of globally hyperbolic maximal anti-de Sitter structures along pinching sequences
Andrea Tamburelli
Let be a closed oriented surface of genus at least . Using the parameterisation of the deformation space of globally hyperbolic maximal anti-de Sitter structures on $S \time…
Regular globally hyperbolic maximal anti-de Sitter structures
Andrea Tamburelli
Let 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}…
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…
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 by the cotangent bundle of the Teichmüller space of , we study how…
Constant mean curvature foliation of globally hyperbolic (2+1)-spacetimes with particles
Qiyu Chen, Andrea Tamburelli
Let be a globally hyperbolic maximal compact -dimensional spacetime locally modelled on Minkowski, anti-de Sitter or de Sitter space. It is well known that admits a uniq…
Constant mean curvature foliation of domains of dependence in
Andrea Tamburelli
We prove that, given an acausal curve in the boundary at infinity of which is the graph of a quasi-symmetric homeomorphism , there exists a unique foliation of its…
Prescribing metrics on the boundary of AdS 3-manifolds
Andrea Tamburelli
We prove that given two metrics and with curvature on a closed, oriented surface of genus , there exists an manifold with smooth, spac…