Add to ORKGWe prove that if Σ is a compact hypersurface in Euclidean space Rn, its boundary lies on the boundary of a convex body C, and meets C orthogonally from the outside, then the total positive curvature of Σ is bigger than or equal to half the area of the sphere Sn−1. Also, we obtain necessary and sufficient conditions for the equality to hold. 1
Abstract. We show that a compact embedded hypersurface with constant ratio of mean curvature functio...
AbstractIt is known that for a sequence {Ωt} of convex sets expanding over the whole hyperbolic spac...
Abstract. The classical Cohn-Vossen inequality states that for any complete 2-dimen-sional Riemannia...
Let M ” be a smooth complete oriented Riemannian manifold of nonnegative sectional curvature, and le...
AbstractIn this article, we prove that every positively curved, complete non-compact hypersurface in...
We prove that every complete connected immersed surface with positive extrinsic cur-vature K in H2 ×...
For a convex domain \(D\) bounded by the hypersurface \(\partial D\) in a space of constant curvatur...
Abstract. We prove that the area of a hypersurface Σ which traps a given volume outside a convex dom...
In this paper we extend Efimov’s Theorem by proving that any complete surface in R3 with Gauss curva...
Abstract. We show that closed hypersurfaces in Euclidean space with nonnegative scalar curvature are...
AbstractIn this article, we prove that every positively curved, complete non-compact hypersurface in...
In this paper we study the regularity of closed, convex surfaces which achieve maximal affine area a...
Abstract. It is proved that a convex hypersurface in a Riemannian manifold of sectional curvature>...
It is still an open question whether a compact embedded hypersurface in the Euclidean space with con...
The following paper considers Alexandrov’s conjecture, that the ratio of surface area to intrinsic d...
Abstract. We show that a compact embedded hypersurface with constant ratio of mean curvature functio...
AbstractIt is known that for a sequence {Ωt} of convex sets expanding over the whole hyperbolic spac...
Abstract. The classical Cohn-Vossen inequality states that for any complete 2-dimen-sional Riemannia...
Let M ” be a smooth complete oriented Riemannian manifold of nonnegative sectional curvature, and le...
AbstractIn this article, we prove that every positively curved, complete non-compact hypersurface in...
We prove that every complete connected immersed surface with positive extrinsic cur-vature K in H2 ×...
For a convex domain \(D\) bounded by the hypersurface \(\partial D\) in a space of constant curvatur...
Abstract. We prove that the area of a hypersurface Σ which traps a given volume outside a convex dom...
In this paper we extend Efimov’s Theorem by proving that any complete surface in R3 with Gauss curva...
Abstract. We show that closed hypersurfaces in Euclidean space with nonnegative scalar curvature are...
AbstractIn this article, we prove that every positively curved, complete non-compact hypersurface in...
In this paper we study the regularity of closed, convex surfaces which achieve maximal affine area a...
Abstract. It is proved that a convex hypersurface in a Riemannian manifold of sectional curvature>...
It is still an open question whether a compact embedded hypersurface in the Euclidean space with con...
The following paper considers Alexandrov’s conjecture, that the ratio of surface area to intrinsic d...
Abstract. We show that a compact embedded hypersurface with constant ratio of mean curvature functio...
AbstractIt is known that for a sequence {Ωt} of convex sets expanding over the whole hyperbolic spac...
Abstract. The classical Cohn-Vossen inequality states that for any complete 2-dimen-sional Riemannia...