Quantization for an elliptic equation with critical exponential growth on compact Riemannian surface without boundary

TL;DR

This paper establishes a quantization phenomenon for elliptic equations with critical exponential growth on compact Riemannian surfaces, extending known Euclidean space results to curved surfaces using blow-up analysis.

Contribution

It proves a new quantization result for elliptic equations with critical exponential growth on Riemannian surfaces, generalizing prior Euclidean space findings.

Findings

Quantization result for elliptic equations on Riemannian surfaces

Extension of Euclidean results to curved surfaces

Application of blow-up analysis techniques

Abstract

In this paper, using blow-up analysis, we prove a quantization result for an elliptic equation with critical exponential growth on compact Riemannian surface without boundary. Similar results for Euclidean space were obtained by Adimurthi-Struwe \cite{Adi-Stru}, Druet \cite{Druet}, Lamm-Robert-Struwe \cite{L-R-S}, Martinazzi \cite{Mart}, Martinazzi-Struwe \cite{Mar-Stru}, and Struwe \cite{Struwe} respectively.