Sobolev Inequalities on K\"ahler manifolds

TL;DR

This paper establishes new Sobolev inequalities on compact K"ahler manifolds with positive Ricci curvature and revisits classical inequalities using traditional methods.

Contribution

It introduces novel Sobolev inequalities specific to K"ahler manifolds and provides a classical proof approach for existing inequalities.

Findings

New Sobolev inequalities on K"ahler manifolds with positive Ricci curvature

Classical proof of existing Sobolev inequalities using Bidaut-Véron approach

Enhanced understanding of geometric analysis on K"ahler manifolds

Abstract

We prove new Sobolev type inequalities on compact K\"ahler manifolds with positive Ricci curvature. A proof of an already existing Sobolev inequality in the classical Bidaut-V\'eron and V\'eron approach is also discussed.