Compact Euclidean space forms

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...

On images of continuous functions from a compact manifold to 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.

Harmonic Morphisms from Three-dimensional Euclidean and Spherical Space Forms

This paper gives a description of all harmonic morphisms from a threedimensional non-simply-connected Euclidean and spherical space form to a surface, by extending the work of Baird-Wood [4, 5] who dealt with the simply-connected case; namely we show that any such harmonic morphism is the composition of a “standard” harmonic morphism and a weakly conformal map. To complete the description we li...

on images of continuous functions from a compact manifold to euclidean space