The evolute of a regular curve in the Lorentz–Minkowski plane is given by the locus of centers of osculating pseudo-circle of the base curve. But the case when a curve has singularities is not very clear. In this paper, we use lightcone frame to define the [Formula: see text]-cusp mixed-type curves and their evolutes in Lorentz–Minkowski plane. In order to attain this goal, we define the [Formula: see text]-cusp non-lightlike curves and their evolutes in Lorentz–Minkowski plane first. Then we study the behaviors of the evolutes of the [Formula: see text]-cusp mixed-type curves at the [Formula: see text]-cusp.

中文翻译：

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Lorentz-Minkowski 平面中 (n,m)-尖点混合型曲线的演化

Lorentz-Minkowski 平面中规则曲线的演化由基曲线的密切伪圆的中心轨迹给出。但是曲线具有奇点的情况不是很清楚。在本文中，我们使用光锥框架来定义[公式：见正文]-尖点混合型曲线及其在 Lorentz-Minkowski 平面中的演化。为了达到这个目标，我们首先定义了[公式：见正文]-尖点非光曲线及其在洛伦兹-闵可夫斯基平面上的演化。然后我们研究[公式：见文本]-尖点混合型曲线在[公式：见文本]-尖点处的演化曲线的行为。