On the existence of constant scalar curvature K\"ahler metric: a new perspective

TL;DR

This paper introduces a novel continuity path connecting constant scalar curvature Kähler metrics to a second order elliptic equation, offering new insights into the geometric and analytical aspects of the problem.

Contribution

It presents a new continuity method linking scalar curvature equations to elliptic equations, expanding the analytical tools available for Kähler geometry.

Findings

Establishment of a new continuity path for scalar curvature equations

Insights into the geometric and analytical structure of Kähler metrics

Potential applications to existence problems in Kähler geometry

Abstract

In this paper, we report a "new" continuity path which links the constant scalar curvature equation to a second order elliptic equation. This is largely an expository article where we describes various aspects of geometry and analysis associated with path.