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arXiv · 1306.3897

The Bochner Formula via Volume Variations

Christopher Lin
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Abstract

In this short paper, we re-derive the Bochner formula for the Laplacian by considering local variations of volume. The derivation is rooted in the fact that the Laplacian of a function measures the volume variation along the flow of the gradient vector of the function. Possible extensions of this approach/technique are also discussed. While the value of this approach may be limited in terms of research, we think it definitely has pedagogical value.

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Christopher Lin. 2013-06-17. The Bochner Formula via Volume Variations. https://arxiv.org/abs/1306.3897

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