The research of caloric morphism

热量态射的研究

• 批准号: 15540153
• 负责人: SHIMOMURA Katsunori
• 金额: $ 1.79万
• 依托单位: IBARAKI UNIVERSITY
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2003
• 资助国家: 日本
• 起止时间: 2003 至 2004
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-15540153/
• 关键词: caloric morphism; Appell transformation; heat equation; 熱方程式

On caloric morphisms between manifolds, we obtained the following results :1.The determination of the caloric morphism which translates the origin on punctured euclidean space of radial riemannian metric in the case that the dimension is greater than 2.2.The determination of the caloric morphism on punctured euclidean space of radial semi-riemannian metric.3.The parametrization of the caloric morphisms in above 2 by the power of the metric.4.The determination of the caloric morphism on two different punctured euclidean space of radial semi-riemannian metric.5.The determination of the caloric morphism on punctured euclidean space of rotation invariant riemannian metric.

关于流形之间的热态射，我们得到了以下结果：1.在维数大于2的情况下，确定了径向黎曼度量的删余欧氏空间上平移原点的热态射; 2.确定了径向半黎曼度量的删余欧氏空间上的热态射; 3.利用度量的幂对上述2中的热态射进行了参数化; 4.确定了径向半黎曼度量的两个不同删余欧氏空间上的热态射; 5.确定了旋转不变黎曼度量的删余欧氏空间上的热态射.

项目成果

Toshio Horiuchi: "Missing terms in generalized Hardy's inequalities and its application"J.Math.Kyoto Univ.. 43(3). 235-265 (2003)

Toshio Horiuchi：“广义哈代不等式中的缺失项及其应用”J.Math.Kyoto Univ.. 43(3)。

α-parabolic bergman spaces

• DOI: 10.18910/7024
• 发表时间: 2005-03
• 期刊: Osaka Journal of Mathematics
• 影响因子: 0.4
• 作者: Masaharu Nishio;Katsunori Shimomura;N. Suzuki

Missing terms in Hardy-Sobolev inequalities and its application.

Hardy-Sobolev 不等式中的缺失项及其应用。

• 发表时间: 2004
• 期刊: Far Fast Journal of Mathematical Sciences 14(3)
• 作者: A.Detalla;T.Horiuchi;H.Ando
• 通讯作者: H.Ando

Toshio Horiuchi, Peter Kumlin: "On the minimal solution for quasilinear degenerate elliptic equation and its blow-up"J.Math.Kyoto Univ.. (印刷中). (2004)

Toshio Horiuchi、Peter Kumlin：“关于拟线性简并椭圆方程及其爆炸的最小解”J.Math.Kyoto Univ..（出版中）。

Caloric morphisms with respect to radial metrics on R^n＼{0}.

相对于 R^n{0} 上的径向度量的热量态射。

• 发表时间: 2003
• 期刊: Math.J.Ibaraki Univ. 35
• 作者: M.Nishio;K.Shimomura;Katsunori Shimomura
• 通讯作者: Katsunori Shimomura