The Bochner Formula via Volume Variations
Differential Geometry
2013-06-18 v1 Analysis of PDEs
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.
Keywords
Cite
@article{arxiv.1306.3897,
title = {The Bochner Formula via Volume Variations},
author = {Christopher Lin},
journal= {arXiv preprint arXiv:1306.3897},
year = {2013}
}
Comments
10 pages, comments and suggestions are welcome