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arXiv · 2501.05699

$L^2$-estimates on flat vector bundles and Prékopa's theorem

Gang Huang·Weiwen Jiang·Xiangsen Qin
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Abstract

In this paper, we will construct Hörmander's $L^2$-estimate of the operator $d$ on a flat vector bundle over a $p$-convex Riemannian manifold and discuss some geometric applications of it. In particular, we will generalize the classical Prékopa's theorem in convex analysis.

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Gang Huang, Weiwen Jiang, Xiangsen Qin. 2025-01-10. $L^2$-estimates on flat vector bundles and Prékopa's theorem. https://arxiv.org/abs/2501.05699

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