From harmonic mappings to Ricci flow due to the Bochner technique

TL;DR

This paper explores the global geometric properties of harmonic mappings and infinitesimal harmonic transformations, applying these insights to Ricci solutions and Ricci flow through geometric analysis and classical theorems.

Contribution

It introduces new applications of harmonic mapping theory to Ricci flow, utilizing the Bochner technique and classical theorems for global geometric analysis.

Findings

Established links between harmonic mappings and Ricci flow behavior

Applied Bochner technique to analyze infinitesimal harmonic transformations

Extended classical theorems to new contexts in geometric analysis

Abstract

The present paper is devoted to the study a global aspect of the geometry of harmonic mappings and, in particular, infinitesimal harmonic transformations, and represents the application of our results to the theory of Ricci solutions and the Ricci flow. These results will be obtained using the methods of Geometric analysis and, in particular, due to theorems of Yau, Li and Schoen on the connections between the geometry of a complete smooth manifold and the global behavior of its subharmonic functions.