Geometric curvature energies

几何曲率能

• 批准号: 64980826
• 负责人: Professor Dr. Heiko von der Mosel
• 金额: --
• 依托单位: Lehrstuhl für Mathematik (Analysis)
• 依托单位国家: 德国
• 项目类别: Research Grants
• 财政年份: 2007
• 资助国家: 德国
• 起止时间: 2006-12-31 至 2012-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/64980826?language=en
• 关键词: Geometric; curvature; energies

The central issue of this research proposal is the study of geometric curvature energies on curves, surfaces, and higher-dimensional objects of low regularity. These energies exhibit self-avoidance and regularizing effects: a finite energy level guarantees and quantifies embeddedness of the geometric object, and leads to higher regularity. There is a variety of geometric curvature energies ranging from hard steric constraints to soft repulsive potentials, such as global curvature, integral versions of Menger curvature, or self-repulsive knot energies. We investigate the analytical properties of these energies and study their behaviour on families of curves or surfaces. The results will be applied to topologically constrained variational problems in the class of embeddings, and we examine the corresponding timedependent geometric flow problems.

本研究提案的中心问题是研究曲线、曲面和低规律性高维物体上的几何曲率能。这些能量表现出自回避和正则化效应：有限的能量水平保证并量化了几何对象的嵌入性，并导致更高的规律性。几何曲率能有多种，从硬空间约束到软排斥势，例如全局曲率、门格尔曲率的积分形式或自排斥结能量。我们研究这些能量的分析特性并研究它们在曲线或曲面族上的行为。结果将应用于嵌入类中的拓扑约束变分问题，并且我们检查相应的时间相关几何流问题。

项目成果

On some knot energies involving Menger curvature

关于涉及门格尔曲率的一些结能量

• DOI: 10.1016/j.topol.2013.05.022
• 发表时间: 2012
• 期刊: Topology and its Applications
• 影响因子: 0.6
• 作者: Marta Szumanska;Paweł Strzelecki;Heiko von der Mosel
• 通讯作者: Heiko von der Mosel

How averaged Menger curvatures control regularity and topology of curves and surfaces

平均门格尔曲率如何控制曲线和曲面的规律性和拓扑

• DOI: 10.1088/1742-6596/544/1/012018
• 发表时间: 2013
• 期刊: Journal of Physics: Conference Series
• 作者: Paweł Strzelecki;Heiko von der Mosel
• 通讯作者: Heiko von der Mosel

Tangent-Point Repulsive Potentials for a Class of Non-smooth m-dimensional Sets in ℝn. Part I: Smoothing and Self-avoidance Effects

第一部分：平滑和自回避效应中一类非平滑 m 维集合的切点排斥势

• DOI: 10.1007/s12220-011-9275-z
• 发表时间: 2011
• 期刊: Journal of Geometric Analysis
• 影响因子: 1.1
• 作者: Paweł Strzelecki;Heiko von der Mosel
• 通讯作者: Heiko von der Mosel

Menger curvature as a knot energy

门格尔曲率作为结能量

• DOI: 10.1016/j.physrep.2013.05.003
• 发表时间: 2013
• 期刊: Physics Reports
• 作者: Paweł Strzelecki;Heiko von der Mosel
• 通讯作者: Heiko von der Mosel