Given some function H（X）,one can find a compact hypersurface in S<sup>n+1</sup>,which ishomeomorphic to S<sup>m</sup>（1）×S<sup>n-m</sup>（1）and whose mean curvature is giv...Given some function H（X）,one can find a compact hypersurface in S<sup>n+1</sup>,which ishomeomorphic to S<sup>m</sup>（1）×S<sup>n-m</sup>（1）and whose mean curvature is given by H（X）.展开更多
In this note, we shall prove an interesting result.Theorem. Let 2 be a piece of surface without an umbilical point in 3-dimensional constant curvature space M<sup>3</sup>（C） and possess a constant mean c...In this note, we shall prove an interesting result.Theorem. Let 2 be a piece of surface without an umbilical point in 3-dimensional constant curvature space M<sup>3</sup>（C） and possess a constant mean curvature C<sub>1</sub> （C<sub>1</sub>】0）. ∑ can be isometric to a piece of the surface ∑<sup>*</sup> without an umbilical point, ∑<sup>*</sup> owning a constant mean curvature C<sub>2</sub>（C<sub>2</sub>】0 and C<sub>1</sub>≠C<sub>2</sub>） in M<sup>3</sup>（C）展开更多
Suppose H~* is a real function in some region of R^3. By prescribing two conditions onH~*, one can find a surface, which is homeomorphic to a primary closed surface with anarbitrary genus in R^3 and whose mean curvatu...Suppose H~* is a real function in some region of R^3. By prescribing two conditions onH~*, one can find a surface, which is homeomorphic to a primary closed surface with anarbitrary genus in R^3 and whose mean curvature is given by H~*.展开更多
文摘Given some function H（X）,one can find a compact hypersurface in S<sup>n+1</sup>,which ishomeomorphic to S<sup>m</sup>（1）×S<sup>n-m</sup>（1）and whose mean curvature is given by H（X）.
文摘In this note, we shall prove an interesting result.Theorem. Let 2 be a piece of surface without an umbilical point in 3-dimensional constant curvature space M<sup>3</sup>（C） and possess a constant mean curvature C<sub>1</sub> （C<sub>1</sub>】0）. ∑ can be isometric to a piece of the surface ∑<sup>*</sup> without an umbilical point, ∑<sup>*</sup> owning a constant mean curvature C<sub>2</sub>（C<sub>2</sub>】0 and C<sub>1</sub>≠C<sub>2</sub>） in M<sup>3</sup>（C）
文摘Suppose H~* is a real function in some region of R^3. By prescribing two conditions onH~*, one can find a surface, which is homeomorphic to a primary closed surface with anarbitrary genus in R^3 and whose mean curvature is given by H~*.
