Add to ORKGAbstract Given a compact n-dimensional immersed Riemannian manifold Mn in some Euclidean space we prove that if the Hausdorff dimension of the singular set of the Gauss map is small, then Mn is homeomorphic to the sphere Sn. Also, we define a concept of finite geometrical type and prove that finite geometrical type hypersurfaces with a small set of points of zero Gauss–Kronecker curvature are topologically the sphere minus a finite number of points. A characterization of the 2n-catenoid is obtained
AbstractWe investigate the Gauss map of a hypersurface in Euclidean n-sphere as an application of th...
It is said that a topologist is a mathematician who can not tell the difference between a doughnut a...
By a triangulated n-manifold we shall mean a simplicial complex whose body is a compact connected me...
International audienceThe hyperbolic Gauss map G of a complete constant mean curvature one surface M...
We prove that a closed surface with a CAT(κ) metric has Hausdorff dimension = 2, and that there are ...
We give a new approach to the study of relations between the Gauss map and compactness properties fo...
Abstract. Let M denote an even-dimensional non-compact hy-perbolic manifold of finite volume. We sho...
Abstract. We consider the bifurcation set of the Gauss map of an immersed n-dimensional manifold Mn ...
In this paper we give a new, and shorter, proof of Huber's theorem which affirms that for a connecte...
An elementary geometrical proof of the fact that the Euler characteristic is the only topological in...
A topological n-manifold is a Hausdorff space which is locally n-Euclidean (like Rn). No progress wa...
A global statement about a compact surface with constant Gaussian curvature is derived by elementary...
Let Mn be an n-dimensional Riemannian manicold which is minimally immersed in a unit sphere Sn+p(1) ...
In this paper we study the following problem: To what extent does the type of the Gauss map of a sub...
Abstract We continue our investigation of the space of geodesic lamina-tions on a surface, endowed w...
AbstractWe investigate the Gauss map of a hypersurface in Euclidean n-sphere as an application of th...
It is said that a topologist is a mathematician who can not tell the difference between a doughnut a...
By a triangulated n-manifold we shall mean a simplicial complex whose body is a compact connected me...
International audienceThe hyperbolic Gauss map G of a complete constant mean curvature one surface M...
We prove that a closed surface with a CAT(κ) metric has Hausdorff dimension = 2, and that there are ...
We give a new approach to the study of relations between the Gauss map and compactness properties fo...
Abstract. Let M denote an even-dimensional non-compact hy-perbolic manifold of finite volume. We sho...
Abstract. We consider the bifurcation set of the Gauss map of an immersed n-dimensional manifold Mn ...
In this paper we give a new, and shorter, proof of Huber's theorem which affirms that for a connecte...
An elementary geometrical proof of the fact that the Euler characteristic is the only topological in...
A topological n-manifold is a Hausdorff space which is locally n-Euclidean (like Rn). No progress wa...
A global statement about a compact surface with constant Gaussian curvature is derived by elementary...
Let Mn be an n-dimensional Riemannian manicold which is minimally immersed in a unit sphere Sn+p(1) ...
In this paper we study the following problem: To what extent does the type of the Gauss map of a sub...
Abstract We continue our investigation of the space of geodesic lamina-tions on a surface, endowed w...
AbstractWe investigate the Gauss map of a hypersurface in Euclidean n-sphere as an application of th...
It is said that a topologist is a mathematician who can not tell the difference between a doughnut a...
By a triangulated n-manifold we shall mean a simplicial complex whose body is a compact connected me...