Conformal invariants of Riemann surfaces and theta functions

黎曼曲面和 theta 函数的共形不变量

• 批准号: 12640156
• 负责人: YAMADA Akira
• 金额: $ 1.6万
• 依托单位: TOKYO GAKUGEI UNIVERSITY
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2000
• 资助国家: 日本
• 起止时间: 2000 至 2001
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-12640156/
• 关键词: Riemann Surface; conformal invariant; thetafunction; Ahlfors function; de Branges; Bloch function; complementary space

In this year the head investigator continued his study of de Branges' complementation space that is closely related to the notion of the sum of kernel fun cfons. Analyzing the proof by de Branges of the Caratheodory-Fejer extension problem on the unit disk, he showed that a lemma about the existence of the contraction concerning an isometry and coisometry is essential in the proof. Using this lemma he showed simple alternative proof of the commutant lilting theorem due to Nagy : Foias. Also, he showed that the necessary and sufficient condition for the existence of the extended interpolation problem due to Ms. Takahashi in Nara Women 's University is obtained from the lemma by using elementary linear algebra.Kubota showed a theorem that extends to the case of Banach spaces of the result obtained by Rosay-Rudin about the stable domains of the holomorphic automorphisms with fixed points on finite dimensional c omplex spaces.Mizoguchi studied the asymptotic behavior of zeros of solutions for parabolic equations on the real line, and she proved that the zeros remain finite for a fixed blowup time.Masumoto gave a simple alternative proof of the result alrea dy obtained by him that extremal lengths of homology classes on closed Riemann surfaces of finite positive genus satisfy an algebraic equation.Yanagihara studied the variability region of the values f(a) at a fixed point for normalized Bloch functions f(z) on the unit disk. He determined its shape when the derivative at the origin is sufficiently small.

今年，首席调查员继续研究了De Branges的互补空间，该空间与内核Fun CFON的概念密切相关。通过De Branges分析单位磁盘上的Caratheodory-Fejer扩展问题的证明，他表明，关于等距和共轴测图的收缩存在的引理在证明中至关重要。他使用这种引理显示了由于纳吉（Nagy：Foias）而导致的换向物定理的简单替代证明。此外，他还表明，通过使用基本线性代数来获得纳拉妇女大学中高桥女士在纳拉妇女大学中存在延长的插值问题的必要条件。 Mizoguchi研究了真正线上抛物线方程的解决方案零的渐近行为，她证明了零在固定的爆炸时间中仍然有限。Masumoto提供了一个简单的替代证明Alrea dy的结果的简单替代证明了Alrea dy dy的最大程度上的necialge anderge andiragy ander ander andragy andragy andragy andragy andragy andragy andragy andragy andragy andrage andrage andrage andrage andrage andrage andrage andrage andragy andragy andrie andry andriper nir的结果的替代证明。研究了单位磁盘上归一化BLOCH函数F（Z）的固定点的值F（a）的可变性区域。当起源处的衍生物足够小时，他确定了其形状。

项目成果

Hiroshi Yanagihara: "On the growth of Bloch functions"Com plex Variables. 44. 103-115 (2001)

Hiroshi Yanagihara：“论布洛赫函数的增长”复杂变量。

Noriko Mizoguchi: "Life span of solutions for a semilinear parabolic problem with small diffusion"J. Math. Anal. Appl. 261. 350-368 (2001)

沟口纪子：“小扩散半线性抛物线问题解的寿命”J.

Makoto Masumoto: "Hyperbolic lengths and conformal embeddmgs of Riemann surfaces"lsrael J. Math. 116. 77-92 (2001)

Makoto Masumoto：“黎曼曲面的双曲长度和共形嵌入”lsrael J. Math。

Makoto Masumoto: "Extremal lengths of homology classes on compact Riemann surfaces"Nonlinear Anal. 47・8. 5491-5500 (2001)

Makoto Masumoto：“紧致黎曼曲面上同调类的极值长度”非线性分析 47・8。

Akira Yamada: "Ahlfors functions on compact bordered Riemann surfaces"J. Math. Soc. Japan. 53・2. 261-283 (2001)

Akira Yamada：“紧凑边界黎曼曲面上的 Ahlfors 函数”J. 261-283。