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arXiv · 2210.17137

Split-harmonic maps and the interpolation problem for timelike minimal surfaces

Sreedev Manikoth
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Abstract

The singular Bj\" orling problem and its solution for timelike minimal surfaces is a well-known result in minimal surface theory. In this article, we give a different proof of this theorem using split-harmonic maps. This is motivated by a similar solution of the singular Björling problem for maximal surfaces using harmonic maps. As an application, we study the problem of interpolating a given split-Fourier curve to a point by a timelike minimal surface. This is inspired by an analogous result for maximal surfaces. We also solve the problem of interpolating a given split-Fourier curve to another specified split-Fourier curve by a timelike minimal surface.

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Sreedev Manikoth. 2023-04-24. Split-harmonic maps and the interpolation problem for timelike minimal surfaces. https://arxiv.org/abs/2210.17137

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