In this article, we prove that any complete finite index hypersurface in the hyperbolic space H4（-1）（H5（-1）） with constant mean curvature H satisfying H2 6634 （H2 114785 respectively） must be compact. Speciall...In this article, we prove that any complete finite index hypersurface in the hyperbolic space H4（-1）（H5（-1）） with constant mean curvature H satisfying H2 6634 （H2 114785 respectively） must be compact. Specially, we verify that any complete and stable hypersurface in the hyperbolic space H4（-1） （resp. H5（-1）） with constant mean curvature H satisfying H2 6643 （resp. H2 114785 ） must be compact. It shows that there is no manifold satisfying the conditions of some theorems in [7, 9].展开更多
In this paper,we will discuss some properties of the(n,m)-spherical fuctions on the Lie group G=SL(2, R),and obtain the decomposition of f in C_c^4(G)into these functions.Also we give the Fourier inversion formula for...In this paper,we will discuss some properties of the(n,m)-spherical fuctions on the Lie group G=SL(2, R),and obtain the decomposition of f in C_c^4(G)into these functions.Also we give the Fourier inversion formula for the(n,m)-spherical functions in C_c^3(G).展开更多
基金supported by NSFC (10901067)partially supported by NSFC (10801058) and Hubei Key Laboratory of Mathematical Sciences
文摘In this article, we prove that any complete finite index hypersurface in the hyperbolic space H4（-1）（H5（-1）） with constant mean curvature H satisfying H2 6634 （H2 114785 respectively） must be compact. Specially, we verify that any complete and stable hypersurface in the hyperbolic space H4（-1） （resp. H5（-1）） with constant mean curvature H satisfying H2 6643 （resp. H2 114785 ） must be compact. It shows that there is no manifold satisfying the conditions of some theorems in [7, 9].
文摘In this paper,we will discuss some properties of the(n,m)-spherical fuctions on the Lie group G=SL(2, R),and obtain the decomposition of f in C_c^4(G)into these functions.Also we give the Fourier inversion formula for the(n,m)-spherical functions in C_c^3(G).
