The Existence of Pseudoharmonic Maps For Small Horizontal Energy

TL;DR

This paper proves the existence of pseudoharmonic maps from closed pseudo-Hermitian manifolds to Riemannian manifolds when starting with small initial horizontal energy, advancing understanding of geometric flows in complex structures.

Contribution

It establishes the existence of pseudoharmonic maps under small initial energy conditions, a novel result in the study of pseudo-Hermitian geometry.

Findings

Existence of pseudoharmonic maps with small initial horizontal energy

Extension of pseudoharmonic heat flow theory to new geometric settings

Insights into the behavior of geometric flows on pseudo-Hermitian manifolds

Abstract

In this paper, we consider the pseudoharmonic heat flow with small initial horizontal energy and give the existence of pseudoharmonic maps from closed pseudo-Hermitian manifolds to closed Riemannian manifolds.