We describe a convex relaxation for the Gilbert-Steiner problem both in $R^d$ and on manifolds, extending the framework proposed in [9], and we discuss its sharpness by means of calibration type arguments. The minimization of the resulting problem is then tackled numerically and we present results for an extensive set of examples. In particular we are able to address the Steiner tree problem on surfaces.

中文翻译：

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吉尔伯特-施泰纳问题的凸方法

我们在 $R^d$ 和流形上描述了 Gilbert-Steiner 问题的凸松弛，扩展了 [9] 中提出的框架，并且我们通过校准类型参数讨论了它的锐度。然后以数值方式解决由此产生的问题的最小化，并且我们提供了大量示例的结果。特别是我们能够解决表面上的 Steiner 树问题。