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Funktsional'nyi Analiz i ego Prilozheniya, 2025, Volume 59, Issue 2, Pages 25–45
DOI: https://doi.org/10.4213/faa4245 (Mi faa4245) 		 
Interpolation by maximal surfaces

Rukmini Deya, Rahul Kumar Singhb

a International Center for Theoretical Sciences, Bengaluru, India
b Department of Mathematics, Indian Institute of Technology Patna, Bihta, India
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DOI: https://doi.org/10.4213/faa4245
Abstract: In this article, we use the inverse function theorem for Banach spaces to interpolate a given real analytic spacelike curve $a$ in the Lorentz–Minkowski space $\mathbb{L}^3$ to another real analytic spacelike curve $c$, which is “close” enough to $a$ in a certain sense, by constructing a maximal surface containing them. Throughout this study, the Björling problem and Schwarz's solution to it play pivotal roles.
Keywords: Plateau's problem, maximal surfaces, Björling problem.
Funding agency Grant number
International Centre for Theoretical Sciences ICTS/gtl2018/06
Department of Atomic Energy, India RTI4001
MATRICS MTR/2023/000990
This research was supported in part by the International Centre for Theoretical Sciences (ICTS) – Bangalore, for participating in the program – Geometry and Topology for Lecturers (Code: ICTS/gtl2018/06). Rukmini Dey would like to acknowledge the support of the Department of Atomic Energy, Government of India under project no. RTI4001. Rahul Kumar Singh would like to acknowledge the external grant he has obtained, namely MATRICS (File No. MTR/2023/000990), which has been sanctioned by the SERB.
Received: 05.08.2024
Revised: 02.01.2025
Accepted: 13.01.2025
Published: 28.05.2025
English version:
Functional Analysis and Its Applications, 2025, Volume 59, Issue 2, Pages 126–141
DOI: https://doi.org/10.1134/S1234567825020041
Bibliographic databases:
Document Type: Article
MSC: 53A35, 53B30
Language: Russian
Citation: Rukmini Dey, Rahul Kumar Singh, “Interpolation by maximal surfaces”, Funktsional. Anal. i Prilozhen., 59:2 (2025), 25–45; Funct. Anal. Appl., 59:2 (2025), 126–141
Citation in format AMSBIB
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