A heat flow for the critical Trudinger-Moser functional on a closed Riemann surface (Q2140586)

In this paper, the authors propose a heat flow for the critical Trudinger-Moser functional on a closed Riemann surface (\(\Sigma\), g). They prove its short time existence and long time existence and obtain the convergence of the flow in \(H^2(\Sigma)\) along some sequence of times \(t_n\to +\infty\). Moreover, the limit function is a critical point of the Trudinger-Moser functional under certain constraint.