Calculus of Variation and Geometric Structures on Manifolds

首席研究员Yoe Itokawa在与Shiohama Katsuhiro Shiohama的联合研究项目中证明了截面曲率为正的完备非紧流形中的完全极小变差必然有无界像。关于周围空间只有非负曲率的情况，首席研究员已经得到了一些部分结果，但他仍然没有决定是公布后者的结果还是等待进一步的信息。在另一项工作中，这一次是与Ryoichi Kobayashi一起，首席研究员对非负Ricci曲率流形的&Planck常数&gt；-1维同调群进行了分类，在一些相对较弱的条件下，关于它们的横截面大小的增长率。最后的结果被描述在论文《开流形中的电流最小化和非负Ricci曲线的Planck常数&gt；-1同调》中。调查者Masaru Nishihara继续他关于完备局部凸空间E上的弱连续多项式到其对偶空间E的可扩性的研究。他在第六届国际复变分析学术讨论会论文集上发表了《关于无限维空间中全纯函数的延拓》一文。调查者西田信亚研究了超曲和椭圆型耦合偏微分方程组的S。他证明了熵函数的存在等价于系统的同时可对角化，并且在这种条件下，经典技巧可以用来建立解的短期存在性。此外，他还证明了在稳定性假设下，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.