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，正截面曲率的完全非紧流形中的完全最小簇必然具有无界图像。首席研究员已经获得了有关环境空间仅具有非负曲率的情况的部分结果，但他尚未决定是否发布后者结果或等待进一步的信息。在另一项工作中，这次是与 Ryoichi Kobayashi 合作，首席研究员在横截面尺寸增长率相对较弱的条件下对非负里奇曲率流形的<普朗克常数>-1 维同调群进行了分类。最后的结果在论文“Minimizing currents in open局面和<普朗克常数>-1非负里奇曲线m的同源性”中进行了描述。研究者Masaru Nishihara继续研究弱连续多项式在复局部凸空间E上的可延展性双空间E”。他在第六届国际复分析学术研讨会论文集上发表了论文“论无限维空间中的全纯函数的扩展”。研究员 Sinya Nishibata 研究了耦合双曲和椭圆 P.D.E. 系统。他证明了熵函数的存在性等价于系统的联立对角性，并且在这种条件下，可以使用经典技术来建立解的短期存在性。此外，他还表明，在稳定性假设下，长期解也存在，并且当 t 趋于*时，它们收敛到平衡状态。