Related papers: A holomorphic representation formula for parabolic…

We derive geometric formulas for the mass of asymptotically hyperbolic manifolds using coordinate horospheres. As an application, we obtain a new rigidity result of hyperbolic space: if a complete asymptotically hyperbolic manifold has…

In this paper we analyze the notion of morphisms of rings of superfunctions which is the basic concept underlying the definition of supermanifolds as ringed spaces (i.e. following Berezin, Leites, Manin, etc.). We establish a representation…

We develop isometry and inversion formulas for the Segal--Bargmann transform on odd-dimensional hyperbolic spaces that are as parallel as possible to the dual case of odd-dimensional spheres.

This paper derives an explicit formula for Branson's Q-curvature in even-dimensional conformal geometry. The ingredients in the formula come from the Poincare metric in one higher dimension; hence the formula is called holographic. When…

We give an explicit classification of the cominuscule parabolic subalgebras of all complex simple finite dimensional Lie superalgebras.

We prove the existence of a hyperbolic surface spread over the sphere for which the projection map has all its singular values on the extended real line, and such that the preimage of the extended real line under the projection map is…

Isotopic pairs and their representations are considered in a general framework of the vector superalgebra. Numerous examples of finite-dimensional and infinite-dimensional isotopic pairs are discussed. Several types of their representations…

We construct examples of hyperbolic rational homology spheres and hyperbolic knot complements in rational homology spheres containing closed embedded totally geodesic surfaces.

We propose a new method for constructing partially hyperbolic diffeomorphisms on closed manifolds. As a demonstration of the method we show that there are simply connected closed manifolds that support partially hyperbolic diffeomorphisms.

We provide an explicit description of all rigid hypersurfaces that are equivalent to a Heisenberg sphere. These hypersurfaces are determined by 4 real parameters. The defining equations of the rigid spheres can also be viewed as the…

This is a survey article about parabolic bundles and parabolic Higgs bundles.

A new kind of deformed calculus was introduced recently in studying of parabosonic coordinate representation. Based on this deformed calculus, a new deformation of Legendre polynomials is proposed in this paper, some properties and…

The parametric representation is given to the multisoliton solution of the Camassa-Holm equation. It has a simple structure expressed in terms of determinants. The proof of the solution is carried out by an elementary theory of…

In this paper, we explicitly construct the Calabi composition of multiple affine hyperspheres possibly including some points viewing as 0-dimensional hypersheres. Then we compute all the basic affine invariants of the composed affine…

This paper introduces the notion of $k$-isoparametric hypersurface in an $(n+1)$-dimensional Riemannian manifold for $k=0,1,...,n$. Many fundamental and interesting results (towards the classification of homogeneous hypersurfaces among…

It is shown that for n bigger than 1, the group of holomorphic isometries of the n dimensional complex hyperbolic space does not admit non-elementary representations into the group of isometries of the infinite dimensional real hyperbolic…

We give a new method to prove in a uniform and easy way various transformation formulas for Gauss hypergeometric functions. The key is Jacobi's canonical form of the hypergeometric differential equation. Analogy for $q$-hypergeometric…

We show that for every smooth hyperbolic polynomial h there is another hyperbolic polynomial q such that qh has a definite determinantal representation. This is proved by considering sum-of-squares decompositions of certain bilinear forms…

In this paper we compute the Galois groups of basic hypergeometric equations.

We give a decomposition formula for computing the state polytope of a reducible variety in terms of the state polytopes of its components.