A decomposition result for a singular elliptic equation on compact Riemannian manifolds

TL;DR

This paper establishes a decomposition theorem for bounded energy solutions of a singular elliptic equation on compact Riemannian manifolds, advancing understanding of solution structures in geometric analysis.

Contribution

It introduces a novel decomposition result for solutions of singular elliptic equations on compact Riemannian manifolds, which was not previously known.

Findings

Decomposition theorem for bounded energy solutions

Application to singular elliptic equations on manifolds

Enhanced understanding of solution behavior in geometric contexts

Abstract

On compact Riemannian manifolds, we prove a decomposition theorem for arbitrarily bounded energy sequence of solutions of a singular elliptic equation.