Abstract
This chapter is devoted to a geometric application of the improved Bochner inequality, the Bakry–Ledoux isoperimetric inequality (also called the Gaussian isoperimetric inequality). This is one of the most important geometric applications of the Γ-calculus. The asymptotic behavior of (nonlinear or linearized) heat semigroups for large time will play an essential role. A related analysis also shows the Poincaré–Lichnerowicz inequality.
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Ohta, Si. (2021). Bakry–Ledoux Isoperimetric Inequality. In: Comparison Finsler Geometry. Springer Monographs in Mathematics. Springer, Cham. https://doi.org/10.1007/978-3-030-80650-7_15
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DOI: https://doi.org/10.1007/978-3-030-80650-7_15
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