Related papers: Real hypersurfaces in complex and quaternionic hyp…

In this paper we define and study real fibered morphisms. Such morphisms arise in the study of real hyperbolic hypersurfaces in projective space and other hyperbolic varieties. We show that real fibered morphisms are intimately connected to…

Conditions, related to the so-called bending problem are considered for hypersurfaces of a pseudo-Euclidean space. Corresponding theorems are proved.

We study a notion of relative entropy for certain hypersurfaces in hyperbolic space. We relate this quantity to the renormalized area introduced by Graham-Witten[RW99]. We also obtain a monotonicity formula for relative entropy applied to…

In this paper we prove a monotonicity formula for the integral of the mean curvature for complete and proper hypersurfaces of the hyperbolic space and, as consequences, we obtain a lower bound for the integral of the mean curvature and that…

We derive basic differential geometric formulae for surfaces in hyperbolic space represented as envelopes of horospheres. The dual notion of parallel hypersurfaces is also studied. The representation is applied to prove existence and…

We find explicitly all bi-umbilical foliated semi-symmetric hypersurfaces in the four-dimensional Euclidean space.

We study foliations of space forms by complete hypersurfaces, under some mild conditions on its higher order mean curvatures. In particular, in Euclidean space we obtain a Bernstein-type theorem for graphs whose mean and scalar curvature do…

This thesis investigates cusp cross-sections of arithmetic real, complex, and quaternionic hyperbolic $n$--orbifolds. We give a smooth classification of these submanifolds and analyze their induced geometry. One of the primary tools is a…

We prove that any hyperbolic end with particles (cone singularities along infinite curves of angles less than $\pi$) admits a unique foliation by constant Gauss curvature surfaces. Using a form of duality between hyperbolic ends with…

Some integrals of matrix spaces over a quaternionic field have been calculated in this work. The associated volume of hyperbolic matrix spaces over a quaternionic field has also been calculated by making use of these integrals, and it is of…

In this paper, we use the inverse curvature flow to prove a sharp geometric inequality on star-shaped and two-convex hypersurface in hyperbolic space.

Generalizing both hyperbolic framed surfaces and one-parameter families of hyperbolic framed curves, we introduce the concept of hyperbolic generalized framed surfaces and establish their relations in hyperbolic 3-space. We provide the…

In this paper, we present some new properties for p-biharmonic hypersurfaces in Riemannian manifold. We also characterize the p-biharmonic submanifolds in an Einstein space. We construct a new example of proper p-biharmonic hypersurfaces.…

We make observations about constant mean curvature surfaces in Euclidean 3-space and their dual surfaces, and the resulting pairs of surfaces in hyperbolic 3-space under the Lawson correspondence.

We conclude the classification of isoparametric (or equivalently, polar) foliations of complex and quaternionic projective spaces. This is done by investigating the projections of certain inhomogeneous isoparametric foliations of the…

Mean curvature flows of isoparametric submanifolds in Euclidean spaces and spheres have been studied by Liu and Terng. In particular, it was proved that such flows always have ancient solutions. This is also true for mean curvature flows of…

The main purpose of this paper is to give fundamental properties of real lightlike hypersurfaces of paraquaternionic manifolds and to prove the non-existence of real lightlike hypersurfaces in paraquaternionic space forms under some…

We study transformations as in the title with emphasis on those having smooth connected base locus, called "special". In particular, we classify all special quadratic birational maps into a quadric hypersurface whose inverse is given by…

This survey introduces to the hyperbolic unfolding correspondence that links the geometric analysis of minimal hypersurfaces with that of Gromov hyperbolic spaces. Problems caused from hypersurface singularities oftentimes become solvable…

This note provides an alternative proof of a result of Labourie. We show that the two complements of the convex core of a three dimensional quasi-fuchsian hyperbolic manifold may be foliated by embedded hypersurfaces of constant Gaussian…