A bridge connecting convex analysis and complex analysis and L2-estimate of d and ∂¯

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 $\overline{\partial }$-equation or the results we prove in complex analysis.