Calculus of Variation and Geometric Structures on Manifolds

流形上的变分和几何结构微积分

基本信息

批准号：
09640139
负责人：
ITOKAWA Yoe
金额：
$ 1.15万
依托单位：
Fukuoka Institute of Technology
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
1997
资助国家：
日本
起止时间：
1997 至 1998
项目状态：
已结题

项目摘要

The head investigator, Yoe Itokawa, in a joint research project with Katsuhiro Shiohama, has shown that complete minimal varieties in complete noncompact manifolds of positive sectional curvature necessarily have unbounded images. The head investigator has obtained some partial results concerning the case where the ambient spaces have only nonnegative curvature, but he is still undecided whether to publish the latter results or wait for further information. In another work, this time with Ryoichi Kobayashi, the head investigator has classified the <planck's constant>-1 -dimensional homology groups of manifolds of nonnegatively Ricci curvature under some relatively weak conditions on the growth rate of their cross-sectional size. The last results were described in the paper"Minimizing currents in open manifolds and <planck's constant>-1 homology of nonnegatively Ricci curved mThe investigator Masaru Nishihara has continued his investigation on the extendability of weakly continuous polynomials on a comples locally convex space E to its bidual space E". He has published his results in the paper "On extensions of holomorphic functions in infinite dimensional spaces" in Proceedings of the Sixth International Colloquium on Complex Analysis.The investigator Sinya Nishibata has studied systems of coupled hyperbokic and elliptic P.D.E.'s. He was able to prove that the existence of entropy function is equivalent to the simultaneous diagonability of the system and that, under this condition, classical techniques can be used to establish the short-term existence of solutions. In addition, he has also shown that under stability assumptions, long term solutions also exist and when t tends to*, they converge to equilibrium states.

首席研究员Yoe Itokawa在与Katsuhiro Shiohama的联合研究项目中，表明，正面截面曲率的完全非恰当歧管中的完全最小品种必然具有无绑定的图像。有关环境空间仅具有非负曲率的情况，主管研究者已经获得了一些部分结果，但是他仍然不确定是发布后者结果还是等待进一步的信息。在另一项工作中，这次与Ryoichi Kobayashi一起，首席研究员将<Planck的常数> -1-二维同源性组归类为在某些相对较弱的条件下，在其横截面大小的生长速度下，非自止曲率的歧管曲率分类。最后的结果在本文中描述了“最小化开放流形中的电流，<普朗克的常数> -1非校友弯曲的同源性，研究人员Masaru Nishihara继续研究了他对局部在局部将弱连续的多种元素扩展的可扩展性，并在其双层空间e上局部凸出。他在第六次国际复杂分析座谈会会议录中发表了他的结果。他能够证明熵函数的存在等效于系统的对角线性，并且在这种情况下，经典技术可用于确定溶液的短期存在。此外，他还表明，在稳定性假设下，长期解决方案也存在，当t倾向于*时，它们会融合到平衡状态。