$L^2$-estimates on flat vector bundles and Pr\'ekopa's theorem
Differential Geometry
2025-01-13 v1 Complex Variables
Abstract
In this paper, we will construct H\"ormander's -estimate of the operator on a flat vector bundle over a -convex Riemannian manifold and discuss some geometric applications of it. In particular, we will generalize the classical Pr\'ekopa's theorem in convex analysis.
Cite
@article{arxiv.2501.05699,
title = {$L^2$-estimates on flat vector bundles and Pr\'ekopa's theorem},
author = {Gang Huang and Weiwen Jiang and Xiangsen Qin},
journal= {arXiv preprint arXiv:2501.05699},
year = {2025}
}