We answer Mark Kac's famous question, "can one hear the shape of a drum?" in the positive for orbifolds that are 3-dimensional and 4-dimensional lens spaces; we thus complete the answer to this question for orbifold lens spaces in all dimensions. We also show that the coefficients of the asymptotic expansion of the trace of the heat kernel are not sufficient to determine the above results.

中文翻译：

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眼眶透镜空间的等分光度

我们回答 Mark Kac 的著名问题：“人能听到鼓的形状吗？” 在 3 维和 4 维透镜空间的轨道的正中；因此，我们完成了所有维度的双折透镜空间的这个问题的答案。我们还表明，热核轨迹的渐近膨胀系数不足以确定上述结果。