In this work, we consider sequences of C 2 metrics which converges to a C 2 metric in C 0 sense. We show that if the scalar curvature of the sequence is almost non-negative in the integral sense, then the limiting metric has scalar curvature lower bound in point-wise sense.

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We study the spectrum of the Laplacian on the Sierpinski lattices. First, we show that the spectrum of the Laplacian, as a subset of C, remains the same for any p spaces. Second, we characterize all the spectral points on the lattices with a boundary point.

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