Add to ORKGIn this paper we give some geometric characterizations of locally convex hypersurfaces. In particular, we prove that for a given locally convex hypersurface M with boundary, there exists r > 0 depending only on the diameter of M and the principal curvatures of M on its boundary, such that the r-neighbourhood of any given point on M is convex. As an application we prove an existence theorem for a Plateau problem for locally convex hypersurfaces of constant Gauss curvature
A compact subset K ⊂ Cn is said to be polynomially convex if for every point ζ / ∈ K, there exists a...
Abstract. It is proved that a convex hypersurface in a Riemannian manifold of sectional curvature>...
Given a closed, not necessarily convex set D of a Hilbert space, the problem of the existence of a n...
This dissertation is a record of the paper [19] by the author. We study the problem to find strictly...
Abstract We prove the following criterion: a compact connected piecewise-linear hypersurface (withou...
AbstractWe prove the following criterion: a compact connected piecewise-linear hypersurface (without...
Abstract. Let Ω be a bounded planar domain which is convex (although not necessarily strictly convex...
AbstractLet x:M→An+1 be a locally strongly convex hypersurface, given by a strictly convex function ...
An open problem in affine geometry is whether an affine complete locally uniformly convex hypersurfa...
AbstractMotivated by a conjecture of Steinhaus, we consider the mapping F, associating to each point...
Let $N$ be a geodesically convex subset in a convex co-compact hyperbolic manifold $M$ with incompre...
This paper investigates compact, embedded, strictly convex hypersurfaces in the unit sphere and give...
We prove the existence of solutions to the asymptotic Plateau problem for hypersurfaces of prescribe...
Heinrich Tietze has shown that for a closed connected subset of euclidean space being convex is a lo...
We prove that for every metric on the torus with curvature bounded from below by −1 in the sense of ...
A compact subset K ⊂ Cn is said to be polynomially convex if for every point ζ / ∈ K, there exists a...
Abstract. It is proved that a convex hypersurface in a Riemannian manifold of sectional curvature>...
Given a closed, not necessarily convex set D of a Hilbert space, the problem of the existence of a n...
This dissertation is a record of the paper [19] by the author. We study the problem to find strictly...
Abstract We prove the following criterion: a compact connected piecewise-linear hypersurface (withou...
AbstractWe prove the following criterion: a compact connected piecewise-linear hypersurface (without...
Abstract. Let Ω be a bounded planar domain which is convex (although not necessarily strictly convex...
AbstractLet x:M→An+1 be a locally strongly convex hypersurface, given by a strictly convex function ...
An open problem in affine geometry is whether an affine complete locally uniformly convex hypersurfa...
AbstractMotivated by a conjecture of Steinhaus, we consider the mapping F, associating to each point...
Let $N$ be a geodesically convex subset in a convex co-compact hyperbolic manifold $M$ with incompre...
This paper investigates compact, embedded, strictly convex hypersurfaces in the unit sphere and give...
We prove the existence of solutions to the asymptotic Plateau problem for hypersurfaces of prescribe...
Heinrich Tietze has shown that for a closed connected subset of euclidean space being convex is a lo...
We prove that for every metric on the torus with curvature bounded from below by −1 in the sense of ...
A compact subset K ⊂ Cn is said to be polynomially convex if for every point ζ / ∈ K, there exists a...
Abstract. It is proved that a convex hypersurface in a Riemannian manifold of sectional curvature>...
Given a closed, not necessarily convex set D of a Hilbert space, the problem of the existence of a n...