A Weighted Flow related to a Trudinger-Moser Functional on Closed Riemann Surface
摘要
In this paper, with (Σ, g) being a closed Riemann surface, we analyze the possible concentration behavior of a heat flow related to the Trudinger-Moser energy. We obtain a long time existence for the flow. And along some sequence of times tk → + ∞, we can deduce the convergence of the flow in H2(Σ). Furthermore, the limit function is a critical point of the Trudinger-Moser functional under certain constraint.