Characterization of Curvature positivity of Riemannian metrics on flat vector bundles

2020/09/01 by Deng, Fusheng, Zhang, Xujun
#Analysis of PDEs (math.AP) #Complex Variables (math.CV) #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2009.01741

Abstract

We give a characterization of Nakano positivity of Riemannian flat vector bundles over bounded domains D⊂ℝⁿ in terms of solvability of the d equation with certain good L² estimate condition. As an application, we give an alternative proof of the matrix-valued Prekopa's theorem that is originally proved by Raufi. Our methods are inspired by the recent works of Deng-Ning-Wang-Zhou on characterization of Nakano positivity of Hermitian holomorphic vector bundles and positivity of direct image sheaves associated to holomorphic fibrations.

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