板内圆柱几何积分公式

IF 0.6 4区数学 Q3 MATHEMATICS

Differential Geometry and its Applications Pub Date : 2023-10-17 DOI:10.1016/j.difgeo.2023.102066

Ximo Gual-Arnau

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引用次数: 0

摘要

利用圆柱截面给出了Rn域平均曲率积分的新表达式。然后，我们将这些表达式与Rn中仿射子空间不变密度的相应版本相结合，以获得所有平均曲率为？K的积分的伪旋转公式。作为特殊情况，我们给出了R3连通域的体积、面积、平均曲率积分和Euler Poincaré特性的伪旋转积分公式，该连通域的边界是曲面，考虑了R3中中心平面通过不动点的板以及这些板中包含的圆柱体。

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Geometric integral formulas of cylinders within slabs

We present new expressions for the integrals of mean curvature of domains in $R^{n}$ by means of sections with cylinders. Then, we combine these expressions with the corresponding version of the invariant density of affine subspaces in $R^{n}$ , in order to obtain pseudo-rotational formulae for all the integrals of mean curvature of ∂K. As particular cases, we present pseudo-rotational integral formulas for the volume, area, integral of mean curvature, and Euler-Poincaré characteristic of a connected domain of $R^{3}$ , whose boundary is a surface, considering slabs in $R^{3}$ whose central plane passes through a fixed point, and cylinders contained in these slabs.

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来源期刊

Differential Geometry and its Applications 数学-数学

CiteScore

1.00

自引率

20.00%

发文量

审稿时长

6-12 weeks

期刊介绍： Differential Geometry and its Applications publishes original research papers and survey papers in differential geometry and in all interdisciplinary areas in mathematics which use differential geometric methods and investigate geometrical structures. The following main areas are covered: differential equations on manifolds, global analysis, Lie groups, local and global differential geometry, the calculus of variations on manifolds, topology of manifolds, and mathematical physics.