Conformal geometry of curves and surfaces and geometric knot theory

曲线曲面共形几何与几何结理论

• 批准号: 21540089
• 负责人: IMAI Jun
• 金额: $ 2.83万
• 依托单位: Tokyo Metropolitan University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2009
• 资助国家: 日本
• 起止时间: 2009 至 2011
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-21540089/
• 关键词: 微分トポロジー; 結び目のエネルギー; エネルギー; 共形幾何学; 結び目; ポテンシャル

A one-parameter family of renormalized potentials of a compact domain of an Euclidean space is introduced. A couple of sufficient conditions for the uniqueness of a point that gives the maximum(or minimum) value of the potential are given. The renormalization of the average of the squares of the linking numbers of a given knot and random circles, which can be considered as generalization of the renormalization of the integration of a potential on the domain, is studied. It turns out to be invariant under Mobius transformations.

介绍了欧几里得空间紧域的一种单参数重归一化势族。给出了点的唯一性的几个充分条件，使点的势值达到最大值（或最小值）。研究了给定结和随机圆的连接数的平方平均值的重整化问题，这可以看作是定义域上势积分重整化问题的推广。它在莫比乌斯变换下是不变的。

项目成果

Mobius invariant energies and average linking with circle、ESF-EMS-CRM-Pi International Conference on Knots and Links : From Form to Function、Centro di Ricerca Matematica(CRM)

莫比乌斯不变能量和与圆的平均连接，ESF-EMS-CRM-Pi 国际结与连接会议：从形式到功能，Centro di Ricerca Matematica(CRM)

• 发表时间: 2011
• 作者: 田丸博士 ,Jurgen Berndt;Jose Carlos Diaz-Ramos;Akira Yoshioka;Tadashi Aikou;J. O' Hara
• 通讯作者: J. O' Hara

Ideal, best packing, and energy minimizing double helices

理想、最佳包装和能量最小化双螺旋

• 发表时间: 2011
• 期刊: Progress of Theoretical Physics Supplement
• 作者: A.Arvanitoyeorgos;I.Chrysikos;Y.Sakane;Kazuo Habiro;Kazuo Habiro;Hiroshi Tamaru;Kazuo Habiro;Jorg Schurmann and Shoji Yokura;坂根由昌;葉廣和夫;Shoji Yokura;山田拓身;Kazuo Habiro;葉廣和夫;Jorg Schurmann and Shoji Yokura;J. O' Hara;坂根由昌;Jun O'Hara;Tadashi Aikou;山田拓身;葉廣和夫;J. O' Hara
• 通讯作者: J. O' Hara

Energy of knots and related topics

结的能量及相关主题

• 发表时间: 2010
• 作者: Moriuchi;Hiromasa;Jun O'Hara(今井の旧姓)
• 通讯作者: Jun O'Hara(今井の旧姓)

Mobius invariant energies and average linking with circle

莫比乌斯不变能量和平均与圆的联系

• 发表时间: 2011
• 作者: Kanenobu;Taizo;Toru Ohmoto;K. Kanno and K. Taniyama;Akira Yoshioka;Jun O'Hara
• 通讯作者: Jun O'Hara

On the limit sets of spherical CR manifolds

关于球面CR流形的极限集

• 发表时间: 2009
• 期刊: Bull.Inst.Math.Acad.Sin.(N.S.) 4
• 作者: Kamishima;Yoshinobu;Odebiyi;Omolola
• 通讯作者: Omolola