Immersed hypersurfaces with constant Weingarten curvature

Hypersurfaces with Constant Mean Curvature in a Lorentzian Space Form

Hypersurfaces with Constant Scalar Curvature

Let M be a complete two-dimensional surface immersed into the three-dimensional Euclidean space. Then a classical theorem of Hilbert says that when the curvature of M is a non-zero constant, M must be the sphere. On the other hand, when the curvature of M is zero, a theorem of Har tman-Nirenberg [4] says that M must be a plane or a cylinder. These two theorems complete the classification of com...

Curvature Estimates for Weingarten Hypersurfaces in Riemannian Manifolds

We prove curvature estimates for general curvature functions. As an application we show the existence of closed, strictly convex hypersurfaces with prescribed curvature F , where the defining cone of F is Γ+. F is only assumed to be monotone, symmetric, homogeneous of degree 1, concave and of class C, m ≥ 4.

Constant Mean Curvature Hypersurfaces with Constant Δ-invariant

We completely classify constant mean curvature hypersurfaces (CMC) with constant δ-invariant in the unit 4-sphere S 4 and in the Euclidean 4-space E 4 .

hypersurfaces with constant mean curvature in a lorentzian space form