Related papers: Inhomogeneous isoparametric hypersurfaces in compl…
We characterize homogeneous hypersurfaces in complex space forms which arise as critical points of a higher order energy functional. As a consequence, we obtain existence and non-existence results for $\mathbb{CP}^n$ and $\mathbb{CH}^n$,…
We assign some kind of invariant manifolds to a given integrable PDE (its discrete or semi-discrete variant). First, we linearize the equation around its arbitrary solution $u$. Then we construct a differential (respectively, difference)…
We exhibit a family of homogeneous hypersurfaces in affine space, one in each dimension, generalising the Cayley surface.
Cutting a hyperbolic surface X along a simple closed multi-geodesic results in a hyperbolic structure on the complementary subsurface. We study the distribution of the shapes of these subsurfaces in moduli space as boundary lengths go to…
We investigate the problem of finding smooth hypersurfaces of constant mean curvature in hyperbolic space, which can be represented as radial graphs over a subdomain of the upper hemisphere. Our approach is variational and our main results…
The goal of this paper is to classify parametrically parabolic submanifolds in any codimension. First, we describe the ones that are ruled and show that they are the only parabolic submanifolds that admit an isometric immersion as a…
This paper is devoted to superlensing using hyperbolic metamaterials: the possibility to image an arbitrary object using hyperbolic metamaterials without imposing any conditions on size of the object and the wave length. To this end, two…
We classify the space-like biharmonic surfaces in 3-dimension pseudo-Riemannian space form, and construct explicit examples of proper biharmonic hypersurfaces in general ADS space.
In this note we discuss the problem of existence of para-hyperhermitian structures on compact complex surfaces. We construct examples of para-hypercomplex structures on Inoue surfaces of type $S^{-}$ which do not admit compatible metrics.
We review the properties of hyperbolic metamaterials and show that they are promising candidates as substrates for nano-imaging, nano-sensing, fluorescence engineering and for controlling thermal emission. Hyperbolic metamaterials can…
Motivated by spectral asymptotics for orbital integrals in a relative trace formula, we generalize a number of geometric properties of geodesics in the hyperbolic plane, to maximal flat submanifolds of symmetric spaces of non-compact type.
A symplectic form is called hyperbolic if its pull-back to the universal cover is a differential of a bounded one-form. The present paper is concerned with the properties and constructions of manifolds admitting hyperbolic symplectic forms.…
The relation between the uniformizing equation of the complex hyperbolic structure on the moduli space of marked cubic surfaces and an Appell-Lauricella hypergeometric system in nine variables is clarified.
In this paper we consider ultra-parallel complex hyperbolic triangle groups of type $[m_1,m_2,0]$, i.e. groups of isometries of the complex hyperbolic plane, generated by complex reflections in three ultra-parallel complex geodesics two of…
We determine explicitly the structure of the automorphism group of a parabolic Inoue surface. We also describe the quotients of the surface by typical cyclic subgroups of the automorphism group.
Let X be a smooth cubic hypersurface. We prove that a general cubic surface is isomorphic to a hyperplane section of X .
This article discusses inequalities on lengths of curves on hyperbolic surfaces. In particular, a characterization is given of which topological types of curves and multicurves always have a representative that satisfies a length inequality…
We classify polar actions on complex hyperbolic spaces up to orbit equivalence.
We prove a stability version of the isodiametric inequality on the sphere and in the hyperbolic space.
A unimodular complex surface is a complex 2-manifold X endowed with a holomorphic volume form. A strictly pseudoconvex real hypersurface M in X inherits not only a CR-structure but a canonical coframing as well. In this article, this…