Isometric immersions between spaces forms

空间形式之间的等距沉浸

• 批准号: 11640067
• 负责人: MORI Hiroshi
• 金额: $ 2.18万
• 依托单位: Joetsu University of Education
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 1999
• 资助国家: 日本
• 起止时间: 1999 至 2000
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-11640067/
• 关键词: rotation hypersurfaces; mean curvature; hyperbolic space; stable hypersurfaces; notation hypersurface; staffe hypersurface; C^*-algebra; subshift; dimesion group

Hypersurfaces M^n with constant mean curvature in a Riemannian manifold M^^〜^<n+1> are solutions to the variational problem of minimizing the area function for certain variations ; the admissible variations are only those that leave a certain volume function fixed. This isoperimetric character of the variational problem associated to hypersurfaces with constant mean curvature introduces additional complications in the treatment of stability of such hypersurfaces.There are many complete hypersurfaces with constant mean curvature in Euclidean (n+1)-space R^<n+1> and Euclidean (n+1)-sphere S^<n+1>, but in the hyperbolic (n+1)-space H^<n+1> there have been few results on such hypersurfaces except umbilical ones. First main purpose of this paper is to construct one-parameter families of three distinct type, rotation hypersurfaces with constant mean curvature in H^<n+1>, explicitly.Barbosa, do Carmo and Eschenburg have defined the notion of stability for hypersurfaces M^n with constant mean curvature in a Riemannian manifold M^^〜^<n+1>. The case where M^2 is complete and noncompact is treated by da Silveira. The case where M^n, is compact is treated by Barbosa, do Carmo and Eschenburg. Luo has discussed the stability of complete noncompact hypersurfaces with constant mean curvature in R^<n+1>.Except for the case where H=0 very little is known about stability of complete and noncompact Riemannian hypersurfaces of H^<n+1> with constant mean curvature H, when 3【less than or equal】n. Second main purpose of this paper is to discuss the stability of the hypersurfaces in H^<n+1> with constant mean curvature H.

riemonian歧管中的M^n曲率m ^^〜^<n+1>是对某些变化的区域构度的溶液，该变异性与曲率相关的变体特征引入了曲率相关的变异特征高空曲面是许多完整的高度曲面） - 空间H^<n+1>很少有ombi lical lical of of of第一个主要目的OS。 n在riemannian歧管中的n+^<n+1>在r^ <n+1>中具有束缚平均曲率的紧凑型高度曲面的稳定性在这里h = 0，关于紧凑型非伴动riemannian riemannian Hypersurfaces H^ <n+1>的稳定性很少。 [小于或相等] n。

项目成果

MORI,H.: "Hypersurfaces with constant mean curvature in the hyperbolic space and their global stability"in Mathematics Journal of Toyama University. (to appear).

MORI,H.：“双曲空间中具有恒定平均曲率的超曲面及其全局稳定性”，富山大学数学杂志。

Hiroohi meu: "Hypersurfaces with constant mean curvature on hyperbolic space and their global stability"Mathematical Journal of Togana University. (発表予定). (2001)

Hiroohi meu：“双曲空间上具有恒定平均曲率的超曲面及其全局稳定性”Togana 大学数学杂志（即将出版）。

Hireohi,Mori: "Hypersurfaces with constant man curvature in hyperbolic space and thin global stability"Mathematies Journal of Toyama University. (発表予定). (2001)

Hireohi, Mori：“双曲空间中具有恒定人曲率的超曲面和薄全局稳定性”富山大学数学杂志（即将出版）。

Kengo Matsumoto: "Dimension groups for subshifts and simplicity of the associated C^*-algebra"Journal of the Mathematical Society of Japan. vol.51, No.3. 679-698 (1999)

Kengo Matsumoto：“相关 C^* 代数的次移和简化的维度群”日本数学会杂志。