Harmonic functions possess the mean value property, that is, the value of the function at any point is equal to the average value of the function in a domain that contain this point. It is a very attractive problem to look for analogous results in the fractal context. In this paper, we establish a similar results of the mean value property for the harmonic functions on the higher-dimensional Sierpinski gasket.

中文翻译：

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高维谢尔宾斯基垫片上谐波函数的平均值

调和函数具有均值性，即函数在任一点的值等于该点所在域中函数的平均值。在分形上下文中寻找类似的结果是一个非常有吸引力的问题。在本文中，我们为高维谢尔宾斯基垫片上的调和函数建立了类似的平均值属性结果。