Related papers: Combination of affine deformations on a hyperbolic…

Let X be a compact 4-manifold with boundary. We study the space of hyperk\"ahler triples on X, modulo diffeomorphisms which are the identity on the boundary. We prove that this moduli space is a smooth infinite-dimensional manifold and…

Let X be a smooth projective curve over a field of characteristic p>0. We show that the Hitchin morphism, which associates to a Higgs bundle its characteristic polynomial, has a non-trivial deformation over the affine line. This deformation…

We analyze the asymptotic behavior of certain twisted orbital integrals arising from the study of affine Deligne-Lusztig varieties. The main tools include the Base Change Fundamental Lemma and $q$-analogues of the Kostant partition…

Using the parameterisation of the deformation space of GHMC anti-de Sitter structures on $S \times \mathbb{R}$ by the cotangent bundle of the Teichm\"uller space of $S$, we study how some geometric quantities, such as the Lorentzian…

We proved the contractibility of the deformation space of the geodesic triangulations on a closed surface of negative curvature. This solves an open problem proposed by Connelly et al. in 1983, in the case of hyperbolic surfaces. The main…

We use minimal (or CMC) surfaces to describe 3-dimensional hyperbolic, anti-de Sitter, de Sitter or Minkowski manifolds. We consider whether these manifolds admit ``nice'' foliations and explicit metrics, and whether the space of these…

The SL(2)-character variety X of a closed surface M enjoys a natural complex-symplectic structure invariant under the mapping class group G of M. Using the ergodicity of G on the SU(2)-character variety, we deduce that every G-invariant…

Using the Blaschke-Berwald metric and the affine shape operator of a hypersurface M in the (n+1)-dimensional real affine space we can define some generalized curvature tensor named the Opozda-Verstraelen affine curvature tensor. In this…

In this article, we first introduce the quermassintegrals for compact hypersurfaces with capillary boundaries in hyperbolic space from a variational viewpoint, and then we solve an isoperimetric type problem in hyperbolic space. By…

In this article, we derive off-diagonal estimates of the Bergman kernel associated to tensor- products of the cotangent line bundle defined over a hyperbolic Riemann surface of finite volume.

Since their introduction by Thurston, measured geodesic laminations on hyperbolic surfaces occur in many contexts. In [Mor], we have introduced a notion of flat laminations on surfaces endowed with a half-translation structure (that is a…

In the paper we consider Riemannian surfaces admitting a global expression of the Gauss curvature as the divergence of a vector field. It is equivalent to the existence of a metric linear connection of zero curvature. Such a linear…

Let $X$ be a Hyperk\"ahler manifold, and let $H$ be an ample divisor on $X$. We give a lower bound in terms of the Beauville-Bogomolov form $q(H)$ for the twisted cotangent bundle $\Omega_X \otimes H$ to be pseudoeffective. If $X$ is…

In this paper, firstly, inspired by Nat\'{a}rio's recent work \cite{Na}, we use the isoperimetric inequality to derive some Alexandrov-Fenchel type inequalities for closed convex hypersurfaces in the hyperbolic space $\H^{n+1}$ and in the…

Let M be a cusped 3-manifold, and let T be an ideal triangulation of M. The deformation variety D(T), a subset of which parameterises (incomplete) hyperbolic structures obtained on M using T, is defined and compactified by adding certain…

The moduli space of generalized deformations of a Calabi-Yau hypersurface is computed in terms of the Jacobian ring of the defining polynomial. The fibers of the tangent bundle to this moduli space carry algebra structures, which are…

We study deformations of affine toric varieties. The entire deformation theory of these singularities is encoded by the so-called versal deformation. The main goal of our paper is to construct the homogeneous part of some degree -R of this,…

In two former papers, the authors independently proved that the space of hyperbolic cone-3-manifolds with cone angles less than 2{\pi} and fixed singular locus is locally parametrized by the cone angles. In this sequel, we investigate the…

We study a class of affine manifolds equipped with a flat affine connection $\nabla$ and a global Riemannian metric $g$ that is diagonal in local affine coordinates. These structures are closely related to \emph{Hessian manifolds}, where…

We show some generic (robust) properties of smooth surfaces immersed in the real 3-space (Euclidean, affine or projective), in the neighbourhood of a {\em godron} (term due to R.Thom): an isolated parabolic point at which the (unique)…