A Weighted Flow related to a Trudinger-Moser Functional on Closed Riemann Surface

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 t k → + ∞, we can deduce the convergence of the flow in H 2...

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Bibliographic Details
Published inActa mathematica Sinica. English series Vol. 40; no. 9; pp. 2244 - 2262
Main Author Yu, Peng Xiu
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer Berlin Heidelberg 01.09.2024
Springer Nature B.V
Subjects
Convergence
Critical point
Heat transmission
Mathematical analysis
Mathematics
Mathematics and Statistics
Riemann surfaces
58J05
58J32
heat flow
58J35
Trudinger-Moser inequality
global convergence
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Summary: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 t k → + ∞, we can deduce the convergence of the flow in H 2 (Σ). Furthermore, the limit function is a critical point of the Trudinger-Moser functional under certain constraint.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:1439-8516
1439-7617
DOI:10.1007/s10114-024-2447-0