English

$L^2$-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 L2L^2-estimate of the operator dd on a flat vector bundle over a pp-convex Riemannian manifold and discuss some geometric applications of it. In particular, we will generalize the classical Pr\'ekopa's theorem in convex analysis.

Keywords

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}
}
R2 v1 2026-06-28T21:02:12.945Z