关于\（｛\mathbb｛R｝｝^3\）中曲线缩短流的新单调性公式

IF 1 3区数学 Q1 MATHEMATICS

Annali di Matematica Pura ed Applicata Pub Date : 2023-06-02 DOI:10.1007/s10231-023-01348-5

Hayk Mikayelyan

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引用次数: 0

摘要

对于（｛\mathbb｛R｝｝^3\）中的曲线缩短流，导出了几个新的单调性公式。所有这些都有一个共同的主要特征：“能量”项依赖于位置向量和与切线向量正交的平面之间的角度。第一个公式处理曲线在单位球面上的投影，并计算其长度的导数。第二个公式是G.Huisken经典公式的推广，而第三个公式是作者先前推导的平面曲线的对数项单调性公式的推广。

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$New monotonicity formulas for the curve shortening flow in ${\mathbb {R}}^3$$

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New monotonicity formulas for the curve shortening flow in ${\mathbb {R}}^3$

For the curve shortening flow in ${\mathbb {R}}^3$ several new monotonicity formulas are derived. All of them share one main feature: the dependence of the “energy” term on the angle between the position vector and the plane orthogonal to the tangent vector. The first formula deals with the projection of the curve on the unit sphere, and computes the derivative of its length. The second formula is the generalization of the classical formula of G. Huisken, while the third one is the generalization of the monotonicity formula with logarithmic terms previously derived by the author for planar curves.

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来源期刊

Annali di Matematica Pura ed Applicata 数学-数学

CiteScore

2.10

自引率

10.00%

发文量

审稿时长

>12 weeks

期刊介绍： This journal, the oldest scientific periodical in Italy, was originally edited by Barnaba Tortolini and Francesco Brioschi and has appeared since 1850. Nowadays it is managed by a nonprofit organization, the Fondazione Annali di Matematica Pura ed Applicata, c.o. Dipartimento di Matematica "U. Dini", viale Morgagni 67A, 50134 Firenze, Italy, e-mail annali@math.unifi.it). A board of Italian university professors governs the Fondazione and appoints the editors of the journal, whose responsibility it is to supervise the refereeing process. The names of governors and editors appear on the front page of each issue. Their addresses appear in the title pages of each issue.