$L^2$-estimates on flat vector bundles and Pr\'ekopa's theorem

Gang Huang; Weiwen Jiang; Xiangsen Qin

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arXiv · 2501.05699

$L^2$-estimates on flat vector bundles and Pr\'ekopa's theorem

Gang Huang·Weiwen Jiang·Xiangsen Qin

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Abstract

In this paper, we will construct H\"ormander'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 Pr\'ekopa's theorem in convex analysis.

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BibTeX RIS

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

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