Translators of the Mean Curvature Flow in the Special Linear Group SL(2, R)

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URI: https://hdl.handle.net/10481/103087
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Auteur
López Camino, Rafael; Munteanu, Marian Ioan
Editorial
Springer Nature
Materia
Mean curvature flow
 
Translator
 
Iwasawa decomposition
 
Date
2025-02-28
Referencia bibliográfica
López, R., Munteanu, M.I. Translators of the Mean Curvature Flow in the Special Linear Group . Results Math 80, 62 (2025). [https://doi.org/10.1007/s00025-025-02376-8]
Patrocinador
Funding for open access publishing: Universidad de Granada/CBUA; Partially supported by MINECO/MICINN/ FEDER grant no. PID2023-150727NB-I00; “María de Maeztu” Excellence Unit IMAG, reference CEX2020-001105- M, funded by MCINN/AEI/ 10.13039/ 501100011033/ CEX2020-001105-M; Romanian Ministry of Research, Innovation and Digitization, within Program 1—Development of the national RD system, Subprogram 1.2— Institutional Performance—RDI excellence funding projects, Contract no.11PFE/30.12.2021
Résumé
Translators in the special linear group are surfaces whose mean curvature H and unit normal vector N satisfy , where X is a fixed Killing vector field. In this paper we study and classify those translators that are invariant by a one-parameter group of isometries. By the Iwasawa decomposition, there are three types of such groups. The dimension of the Killing vector fields is 4 and an exhaustive discussion is done for each one of the Killing vector fields and each of the invariant surfaces. In some cases, explicit parametrizations of translators are obtained.
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