Abstract
This chapter is devoted to the main ingredients of our geometric analysis on measured Finsler manifolds, the Bochner–Weitzenböck formula (or the Bochner formula), and the corresponding Bochner inequality, in terms of the nonlinear Laplacian and its linearization introduced in the previous chapter. In the language of the celebrated Γ-calculus à la Bakry et al., the Bochner inequality can be regarded as a nonlinear analogue of the Γ2-criterion.
Coupled with the nonlinear heat flow discussed in the next chapter, the Bochner inequality has fruitful applications including gradient estimates (Chap. 14), isoperimetric inequalities (Chap. 15), and functional inequalities (Chap. 16).
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Ohta, Si. (2021). The Bochner–Weitzenböck Formula. In: Comparison Finsler Geometry. Springer Monographs in Mathematics. Springer, Cham. https://doi.org/10.1007/978-3-030-80650-7_12
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DOI: https://doi.org/10.1007/978-3-030-80650-7_12
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