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In this chapter, we study the convexities \(P_3\) and \(P_3^*\) in more depth. Despite the geodesic convexity being the most traditional, many results of the \(P_3\) and \(P_3^*\) convexities are used to obtain results in the geodesic convexity, mainly related to computational complexity and, therefore, we decided to present them first.

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\(P_3\) and \(P_3^*\) Convexities

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  • 发表日期：

    2025年

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  • Júlio Araújo,
  • Mitre C. Dourado,
  • Fábio Protti,
  • Rudini M. Sampaio

摘要

In this chapter, we study the convexities \(P_3\) and \(P_3^*\) in more depth. Despite the geodesic convexity being the most traditional, many results of the \(P_3\) and \(P_3^*\) convexities are used to obtain results in the geodesic convexity, mainly related to computational complexity and, therefore, we decided to present them first.