Related papers: Parabolicity of invariant Surfaces

We shall investigate flat surfaces in hyperbolic 3-space with admissible singularities, called `flat fronts'. An Osserman-type inequality for complete flat fronts is shown. When equality holds in this inequality, we show that all the ends…

We give a local parametric description of all holomorphic hypersurfaces in complex Euclidean and projective spaces with constant index of relative nullity, together with applications. This is a complex analogue to the parametrization for…

The authors study theoretically reflection on the surface of a metamaterial with a hyperbolic dispersion. It is found that reflection is strongly dependent on how the surface is terminated with respect to the asymptote of the hyperbolic…

We investigate differential geometric properties of a parabolic point of a surface in the Euclidean three space. We introduce the contact cylindrical surface which is a cylindrical surface having a degenerate contact type with the original…

We consider four-dimensional vacuum spacetimes which admit a nonvanishing spacelike Killing field. The quotient with respect to the Killing action is a three-dimensional quotient spacetime $(M,g)$. We establish several results regarding…

We classify complex projective surfaces with an automorphism of positive entropy for which the unique invariant measure of maximal entropy is absolutely continuous with respect to Lebesgue measure.

We classify complete biharmonic surfaces with parallel mean curvature vector field and non-negative Gaussian curvature in complex space forms.

We prove an inequality bounding the renormalized area of a complete minimal surface in hyperbolic space in terms of the conformal length of its ideal boundary.

We investigate geometric properties of homogeneous parabolic geometries with generalized symmetries. We show that they can be reduced to a simpler geometric structures and interpret them explicitly. For specific types of parabolic…

We discuss the property of the number density of a fluid of particles living in a curved surface without boundaries to be constant in the thermodynamic limit. In particular we find a sufficient condition for the density to be constant along…

We use the general theory developed in our article arXiv:1208.5510 in the setting of parabolic geometries to reprove known results on special infinitesimal automorphisms of projective and conformal geometries.

This paper examines the geometry of left-invariant vector fields on five-dimensional, simply connected, nilpotent Lie groups equipped with left-invariant Riemannian metrics. Using the canonical identification between the Lie algebra and the…

We construct a special class of spacelike surfaces in the Minkowski 4-space which are one-parameter systems of meridians of the rotational hypersurface with lightlike axis and call these surfaces meridian surfaces of parabolic type. They…

In the present paper we classify curves and surfaces in Euclidean $3-$space which make constant angle with a certain Killing vector field. Moreover, we characterize the catenoid and Dini's surface in terms of constant angle surfaces.

We investigate the existence, convergence and uniqueness of modified general curvature flow of convex hypersurfaces in hyperbolic space with a prescribed asymptotic boundary.

Given a complete hypersurface isometrically immersed in an ambient manifold, in this paper we provide a lower bound for the norm of the mean curvature vector field of the immersion assuming that: 1) The ambient manifold admits a Killing…

The current paper is devoted to the study of integral curves of constant type in parabolic homogeneous spaces. We construct a canonical moving frame bundle for such curves and give the criterium when it turns out to be a Cartan connection.…

We prove a Gauss-Bonnet formula for the extrinsic curvature of complete surfaces in hyperbolic space under some assumptions on the asymptotic behaviour. The result is given in terms of the measure of geodesics intersecting the surface…

The main result is that every complete finite area hyperbolic metric on a sphere with punctures can be uniquely realized as the induced metric on the surface of a convex ideal polyhedron in hyperbolic 3-space. A number of other observations…

Symmetries and the corresponding fields of differential invariants of the inviscid flows on a curve are given. Their dependence on thermodynamic states of media is studied, and a classification of thermodynamic states is given.