We construct a surface that is obtained from the octahedron by pushing out four of the faces so that the curvature is supported in a copy of the Sierpinski gasket (SG) in each of them, and is essentially the self similar measure on SG. We then compute the bottom of the spectrum of the associated Laplacian using the finite element method on polyhedral approximations of our surface, and speculate on the behavior of the entire spectrum.

中文翻译：

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具有分形曲率的凸面

我们通过推出四个面来构造一个从八面体获得的曲面，以便曲率在每个面中的一个谢尔宾斯基垫圈 (SG) 的副本中得到支持，并且本质上是 SG 上的自相似测量。然后，我们使用有限元方法对我们的表面的多面体近似计算相关拉普拉斯算子的谱底，并推测整个谱的行为。