Complete hypersurfaces with constant scalar curvature in a sphere
In this paper, by using Cheng-Yau’s self-adjoint operator , we study the complete hypersurfaces in a sphere with constant scalar curvature.
In this paper, by using Cheng-Yau’s self-adjoint operator , we study the complete hypersurfaces in a sphere with constant scalar curvature.
We show that there exists a complete minimal surface immersed into which is conformally equivalent to a compact hyperelliptic Riemann surface of genus three minus one point. The end of the surface is of Enneper type and its total curvature is .
In this paper we review some topics on the theory of complete minimal surfaces in three dimensional Euclidean space.
In this paper we construct complete minimal surfaces of arbitrary genus in with one, two, three and four ends respectively. Furthermore the surfaces lie between two parallel planes of .
Let Mⁿ (n ≥ 3) be an n-dimensional complete super stable minimal submanifold in with flat normal bundle. We prove that if the second fundamental form A of M satisfies , where α ∈ [2(1 - √(2/n)), 2(1 + √(2/n))], then M is an affine n-dimensional plane. In particular, if n ≤ 8 and , d = 1,3, then M is an affine n-dimensional plane. Moreover, complete strongly stable hypersurfaces with constant mean curvature and finite -norm curvature in ℝ⁷ are considered.
In this paperwe give new existence results for complete non-orientable minimal surfaces in ℝ3 with prescribed topology and asymptotic behavior
In this note we show that any complete Kähler (immersed) Euclidean hypersurface must be the product of a surface in with an Euclidean factor .