A bridge connecting convex analysis and complex analysis and $L^2$-estimate of $d$ and $\bar\partial$

Fusheng Deng; Jinjin Hu; Weiwen Jiang; Xiangsen Qin

A bridge connecting convex analysis and complex analysis and $L^2$-estimate of $d$ and $\bar\partial$

Complex Variables 2025-03-04 v2

Authors: Fusheng Deng , Jinjin Hu , Weiwen Jiang , Xiangsen Qin

Abstract

We propose a way to connect complex analysis and convex analysis. As applications, we derive some results about $L^2$ -estimate for $d$ -equation and prove some curvature positivity related to convex analysis from well known $L^2$ -estimate for $\bar\partial$ -equation or the results we prove in complex analysis.

Keywords

convex analysis complex analysis L^2 estimate d-equation bar partial equation curvature positivity

Cite

@article{arxiv.2405.08559,
  title  = {A bridge connecting convex analysis and complex analysis and $L^2$-estimate of $d$ and $\bar\partial$},
  author = {Fusheng Deng and Jinjin Hu and Weiwen Jiang and Xiangsen Qin},
  journal= {arXiv preprint arXiv:2405.08559},
  year   = {2025}
}

Comments

To appear in Journal of Functional Analysis

A bridge connecting convex analysis and complex analysis and $L^2$-estimate of $d$ and $\bar\partial$

Abstract

Keywords

Cite

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