A heat flow for the critical Trudinger-Moser functional on a closed Riemann surface. (English) Zbl 1493.58008
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.
Reviewer: Bo Liu (Bures-sur-Yvette)
MSC:
| 58J05 | Elliptic equations on manifolds, general theory |
| 58J32 | Boundary value problems on manifolds |
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