Ricci Curvature and Bochner Formulas for Martingales

DOI10.1002/cpa.21736zbMath1393.60042arXiv1608.04371OpenAlexW2963230770MaRDI QIDQ4576031

Robert Haslhofer, Aaron Naber

Publication date: 12 July 2018

Published in: Communications on Pure and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1608.04371

zbMATH Keywords

martingalesRicci curvatureHessian estimatesBochner formulas

Mathematics Subject Classification ID

Martingales with continuous parameter (60G44) Local Riemannian geometry (53B20)

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Characterizations of the upper bound of Bakry-Emery curvature ⋮ Spectral gap on Riemannian path space over static and evolving manifolds ⋮ An optimal transport formulation of the Einstein equations of general relativity ⋮ Bochner formulas, functional inequalities and generalized Ricci flow ⋮ Characterization of pinched Ricci curvature by functional inequalities ⋮ Pointwise characterizations of curvature and second fundamental form on Riemannian manifolds ⋮ Functional inequalities on path space of sub-Riemannian manifolds and applications ⋮ Identifying constant curvature manifolds, Einstein manifolds, and Ricci parallel manifolds ⋮ Brownian motion on Perelman's almost Ricci-flat manifold ⋮ Differential Harnack inequalities on path space ⋮ Hitting estimates on Einstein manifolds and applications ⋮ A Bochner formula on path space for the Ricci flow

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