About the geometry of the Cassini oval, its non-convexity degree and $\varepsilon$-offset layer

O. Kuvshinov
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Abstract

The paper studies the geometry of a closed nonconvex smooth simply connected curve on a plane — of the Cassini oval, as well as the geometry of the $\varepsilon$-layer around the set whose boundary is the Cassini oval. Various analytical representations of the $\varepsilon$-layer boundary are formed, and special points of this boundary are described. The measure of nonconvexity $\alpha$ of a simply connected set whose boundary is the Cassini oval is determined, and the angular characteristic of nonconvexity of its $\varepsilon$-neighborhood is defined.
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关于卡西尼椭圆的几何,它的非凸度和$\varepsilon$偏移层
研究了卡西尼椭圆平面上的闭非凸光滑单连通曲线的几何性质,以及以卡西尼椭圆为边界的集合周围$\varepsilon$ -层的几何性质。形成了$\varepsilon$层边界的各种解析表示,并描述了该边界的特殊点。确定了以卡西尼椭圆为边界的单连通集的非凸性测度$\alpha$,并定义了其$\varepsilon$邻域的非凸性的角特性。
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