Construction of the fundamental solution for equations of parabolic type and its applications to geometric problems

抛物型方程基本解的构造及其在几何问题中的应用

• 批准号: 09640213
• 负责人: IWASAKI Chisato
• 金额: $ 1.73万
• 依托单位: Himeji 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
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-09640213/
• 关键词: paroboloc differential eqation; fundamental solution; pseudo-differential operator; Riemann Roch theorem; Gauss-Bonnet-Chern theorem; symbolic calculus; curvature of manifold; Kaehler manifold; スペクトル; トッドクラス; リーマン多様体

1. An analytical proof of the local version of the Gauss-Banner-Chern Theorem has been obtained by Chisato Iwasaki in a paper titled A proof of the Gauss Bonnet-Chern Theorem by the symbolic calculus of pseudo-differential operators, only calculating the main term of the fundamental solution for equation of parabolic type, which was constructed by the new method.2. Applying the above method to manifolds with boundary, we obtained the relation of spectrum of Laplacian and curvatures of manifolds, according to the plan of 1998. This result is one of extension of that of Gunther-Schiminng on manifolds without boundary. This results was tailked in the conference in Germany.3. Local version of Riemann-Roch Thorem for Kaehler manifolds is obtained, by applying the method of construction of the fundamental solution for the degenerate parabolic equation. This result is presented in both conference at Osaka in 1998 and workshop at Potsdom in 1998.

1. Chisato Iwasaki 在题为 Aproof of the Gauss Bonnet-Chern Theorem by the symbolic calculus of pseudo- Differential Operators, 的论文中得到了局部版本的 Gauss-Banner-Chern 定理的解析证明，仅计算了用新方法构造的抛物型方程基本解的主项。 2.将上述方法应用到有边界流形上，根据1998年的计划，得到了拉普拉斯谱与流形曲率的关系。这个结果是Gunther-Schiming在无边界流形上的推广之一。这一结果在德国会议上得到了尾随。3．应用简并抛物型方程基本解的构造方法，得到了凯勒流形的黎曼-罗赫定理的局部版本。这一结果在 1998 年大阪会议和 1998 年 Potsdom 研讨会上发表。

项目成果

Takao Akahori: "Real analyticity of the canorical deformations of CR-structures" Pacific J.of Math.185. 33-45 (1998)

Takao Akahori：“CR 结构的正则变形的真实分析性”Pacific J.of Math.185。

T.Fukui and J.Sekiguchi: "Eight lines arrangements on the real projective plane and the root system of type E_8" Proe,Third Teck.Conference in Math.377-388 (1998)

T.Fukui 和 J.Sekiguchi：“实射影平面上的八条线排列和 E_8 型根系”Proe，第三次 Teck.数学会议.377-388 (1998)

Takeshi Usa: "An example of Liltration on syzygies induced by meta-Lefs chetz operators" Rpt.Fac.Sci.H,I,T.8. 12-25 (1997)

Takeshi Usa：“元 Lefs chetz 算子引起的 syzygies 的 Liltration 示例”Rpt.Fac.Sci.H,I,T.8。

T.fukui and J.Sekiguchi: "Eight lines arrangements on the real projective plane and the root system of type E_8" Proc. Third Tech.Conference in Math.377-388 (1998)

T.fukui 和 J.Sekiguchi：“实射影平面上的八条线排列和 E_8 型根系”Proc。

Takao Akahori & Kimio Miyajima: "A smoothness of deformations of normal Strongly psendo-conuex CR structures" Kyushu J.of math.52. 413-438 (1998)

赤堀隆雄