15 citations · 50 across the 28 of their papers we have counts for
38 papers
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,…
Convex projective manifolds, symmetric spaces and geometric decompositions
Stefano Riolo, Andrea Seppi, Leone Slavich
We prove that if a closed, indecomposable, properly convex real projective -manifold is geometric or admits a geometric decomposition in the sense of Thurston, then every piece…
Weakly almost-Fuchsian manifolds are nearly-Fuchsian
Manh-Tien Nguyen, Jean-Marc Schlenker, Andrea Seppi
We show that a hyperbolic three-manifold containing a closed minimal surface with principal curvatures in also contains nearby (non-minimal) surfaces with principal cu…
Entire hypersurfaces of constant scalar curvature in Minkowski space
Pierre Bayard, Andrea Seppi
We show that every regular domain in Minkowski space which is not a wedge admits an entire hypersurface whose domain of dependence is an…
Uniqueness and non-uniqueness for the asymptotic Plateau problem in hyperbolic space
Zheng Huang, Ben Lowe, Andrea Seppi
We prove several results on the number of solutions to the asymptotic Plateau problem in . Firstly we discuss criteria that ensure uniqueness. Given a Jordan curve …
The Anti-de Sitter proof of Thurston's earthquake theorem
Farid Diaf, Andrea Seppi
Thurston's earthquake theorem asserts that every orientation-preserving homeomorphism of the circle admits an extension to the hyperbolic plane which is a (left or right) earthquak…
On complete maximal submanifolds in pseudo-hyperbolic space
Andrea Seppi, Graham Smith, Jérémy Toulisse
We provide a full classification of complete maximal -dimensional spacelike submanifolds in the pseudo-hyperbolic space , and we study its applications to Teic…
The multiple fibration problem for Seifert 3-orbifolds
Oliviero Malech, Mattia Mecchia, Andrea Seppi
We conclude the multiple fibration problem for closed orientable Seifert three-orbifolds, namely the determination of all the inequivalent fibrations that such an orbifold may admi…
Completeness of convex entire surfaces in Minkowski 3-space
Francesco Bonsante, Andrea Seppi, Peter Smillie
We prove four results towards a description, in terms of the null support function, of the set of isometric embeddings of the hyperbolic plane into Minkowski 3-space. We show that…
Quasi-Fuchsian manifolds close to the Fuchsian locus are foliated by constant mean curvature surfaces
Diptaishik Choudhury, Filippo Mazzoli, Andrea Seppi
Even though it is known that there exist quasi-Fuchsian hyperbolic three-manifolds that do not admit any monotone foliation by constant mean curvature (CMC) surfaces, a conjecture…
Hypersurfaces of constant Gauss-Kronecker curvature with Li-normalization in affine space
Xin Nie, Andrea Seppi
For convex hypersurfaces in the affine space (), A.-M.\ Li introduced the notion of -normal field as a generalization of the affine normal field. By s…
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…
A remark on one-harmonic maps from a Hadamard surface of pinched negative curvature to the hyperbolic plane
François Fillastre, Andrea Seppi
We show that every one-harmonic map, in the sense of Trapani and Valli, from a Hadamard surface of pinched negative curvature to has image the interior of the convex…
The half-space model of pseudo-hyperbolic space
Andrea Seppi, Enrico Trebeschi
In this note we develop a half-space model for the pseudo-hyperbolic space , for any with . This half-space model embeds isometrically onto the com…
Rigidity of minimal Lagrangian diffeomorphisms between spherical cone surfaces
Christian El Emam, Andrea Seppi
We prove that any minimal Lagrangian diffeomorphism between two closed spherical surfaces with cone singularities is an isometry, without any assumption on the multiangles of the t…
Affine deformations of quasi-divisible convex cones
Xin Nie, Andrea Seppi
For any subgroup of obtained by adding a translation part to a subgroup of which is the fundamental group…
On the Gauss map of equivariant immersions in hyperbolic space
Christian El Emam, Andrea Seppi
Given an oriented immersed hypersurface in hyperbolic space , its Gauss map is defined with values in the space of oriented geodesics of , which…
Character varieties of a transitioning Coxeter 4-orbifold
Stefano Riolo, Andrea Seppi
In 2010, Kerckhoff and Storm discovered a path of hyperbolic 4-polytopes eventually collapsing to an ideal right-angled cuboctahedron. This is expressed by a deformation of the inc…
On the diffeomorphism type of Seifert fibered spherical 3-orbifolds
Mattia Mecchia, Andrea Seppi
It is well known that, among closed spherical Seifert three-manifolds, only lens spaces and prism manifolds admit several Seifert fibrations which are not equivalent up to diffeomo…
Examples of geometric transition in low dimensions
Andrea Seppi
The purpose of this note is to discuss examples of geometric transition from hyperbolic structures to half-pipe and Anti-de Sitter structures in dimensions two, three and four. As…
Anti-de Sitter geometry and Teichmüller theory
Francesco Bonsante, Andrea Seppi
The aim of these notes is to provide an introduction to Anti-de Sitter geometry, with special emphasis on dimension three and on the relations with Teichmüller theory, whose study…
Complete CMC hypersurfaces in Minkowski (n+1)-space
Francesco Bonsante, Andrea Seppi, Peter Smillie
We prove that any regular domain in Minkowski space is uniquely foliated by spacelike constant mean curvature (CMC) hypersurfaces. This completes the classification of entire space…
Geometric transition from hyperbolic to anti-de Sitter structures in dimension four
Stefano Riolo, Andrea Seppi
We provide the first examples of geometric transition from hyperbolic to anti-de Sitter structures in dimension four, in a fashion similar to Danciger's three-dimensional examples.…
Regular domains and surfaces of constant Gaussian curvature in three-dimensional affine space
Xin Nie, Andrea Seppi
Generalizing the notion of domains of dependence in the Minkowski space, we define and study regular domains in the affine space with respect to a proper convex cone. In dimension…