Timelike minimal surface in $\mathbb{E}^3_1$ with arbitrary ends

Priyank Vasu, Rahul Kumar Singh, and Subham Paul

Address:
Department of Mathematics, Indian Institute of Technology Patna, Bihta, Patna-801106, Bihar, India
Department of Mathematics, Indian Institute of Technology Patna, Bihta, Patna-801106, Bihar, India
Department of Mathematics, Indian Institute of Technology Patna, Bihta, Patna-801106, Bihar, India

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Abstract: In this paper, we show the existence of a timelike minimal surface with an arbitrary number of weak complete ends. Then, we discuss the asymptotic behaviour of the simple ends and the topology of the singularity set of the constructed timelike minimal surface.

AMSclassification: primary 53A10; secondary 53C42, 30G35.

Keywords: Timelike minimal surface, bicomplex numbers, timelike minimal surface with ends, complete maximal surface, zero mean curvature surface.

DOI: 10.5817/AM2026-2-75