Calculus of Variation and Geometric Structures on Manifolds

首席研究员Yoe Itokawa在与Katsuhiro Shiohama的一个联合研究项目中证明了正截面曲率的完全非紧流形中的完全极小簇必然有无界像。首席研究员已经获得了一些部分结果的情况下，周围的空间只有非负曲率，但他仍然没有决定是否公布后者的结果或等待进一步的信息。在另一项工作中，这一次与Ryoichi小林，首席调查员已分类的<普朗克常数>-1维同调群的流形的非负里奇曲率在一些相对较弱的条件下的增长率，其横截面的大小。最后的结果在论文“Minimizing currents in open manifolds and <planck's constant>-1 homology of nonnegatively Ricci curved m”中得到了描述。研究者Masaru Nishihara继续研究了复局部凸空间E上的弱连续多项式到其双对偶空间E的可拓性。他的研究成果发表在论文“论扩展的全纯函数在无限维空间”在会议录的第六届国际学术讨论会复分析。调查Sinya Nishibata研究了系统的耦合hyperbokic和椭圆PD E。's.他能够证明熵函数的存在性等同于系统的同时可对角性，并且在此条件下，经典技术可以用来建立解的短期存在性。此外，他还表明，在稳定性假设下，长期解决方案也存在，当t趋于 * 时，它们收敛到平衡状态。

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.