15 citations · 50 across the 28 of their papers we have counts for
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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,…
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 …
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…
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…
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…
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…
Entire surfaces of constant curvature in Minkowski 3-space
Francesco Bonsante, Andrea Seppi, Peter Smillie
This paper concerns the global theory of properly embedded spacelike surfaces in three-dimensional Minkowski space in relation to their Gaussian curvature. We prove that every regu…
Spherical, hyperbolic and other projective geometries: convexity, duality, transitions
François Fillastre, Andrea Seppi
Since the end of the 19th century, and after the works of F. Klein and H. Poincaré, it is well known that models of elliptic geometry and hyperbolic geometry can be given using pro…
Area-preserving diffeomorphism of the hyperbolic plane and K-surfaces in Anti-de Sitter space
Francesco Bonsante, Andrea Seppi
We prove that any weakly acausal curve in the boundary of Anti-de Sitter (2+1)-space is the asymptotic boundary of two spacelike -surfaces, one of which is past-convex and t…
Maximal surfaces in Anti-de Sitter space, width of convex hulls and quasiconformal extensions of quasisymmetric homeomorphisms
Andrea Seppi
We give upper bounds on the principal curvatures of a maximal surface of nonpositive curvature in three-dimensional Anti-de Sitter space, which only depend on the width of the conv…
Spacelike convex surfaces with prescribed curvature in (2+1)-Minkowski space
Francesco Bonsante, Andrea Seppi
We prove existence and uniqueness of solutions to the Minkowski problem in any domain of dependence in -dimensional Minkowski space, provided is contained in the fut…
On Codazzi tensors on a hyperbolic surface and flat Lorentzian geometry
Francesco Bonsante, Andrea Seppi
Using global considerations, Mess proved that the moduli space of globally hyperbolic flat Lorentzian structures on is the tangent bundle of the Teichmüller spa…
Minimal discs in hyperbolic space bounded by a quasicircle at infinity
Andrea Seppi
We prove that the supremum of principal curvatures of a minimal embedded disc in hyperbolic three-space spanning a quasicircle in the boundary at infinity is estimated in a subline…