Multiple solutions of compact $H$-surfaces in Euclidean space

Multiple Solutions of Compact H-surfaces in Euclidean Space

We prove here the multiplicity results for the solutions of compact H-surfaces in Euclidean space. Some minimax methods and topological arguments are used for the existence of such solutions in multiply connected domains.

Characterizations of Slant Ruled Surfaces in the Euclidean 3-space

In this study, we give the relationships between the conical curvatures of ruled surfaces generated by the unit vectors of the ruling, central normal and central tangent of a ruled surface in the Euclidean 3-space E^3. We obtain differential equations characterizing slant ruled surfaces and if the reference ruled surface is a slant ruled surface, we give the conditions for the surfaces generate...

compact hypersurfaces in euclidean space and some inequalities

let (m,g ) be a compact immersed hypersurface of (rn+1,) , λ1 the first nonzeroeigenvalue, α the mean curvature, ρ the support function, a the shape operator, vol (m ) the volume of m,and s the scalar curvature of m. in this paper, we established some eigenvalue inequalities and proved theabove.1) 1 2 2 2 2m ma dv dvn∫ ρ ≥ ∫ α ρ ,2)( )2 2 1 2m 1 mdv s dvn nα ρ ≥ ρ∫ − ∫ ,3) if the scalar curvatu...

Minimal Surfaces in Euclidean Space

Embeddings of Surfaces in Euclidean Three-space