Work

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

Year: 2022

Type: preprint

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.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2210.17137

Author: Manikoth, Sreedev

Institution: Indian Institute of Science Education and Research Pune

Language: English

Topic: Geometric Analysis and Curvature Flows

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: Indian Institute of Science Education and Research Pune, Indian Institute of Science Education and Research Mohali

OpenAlex ID: W4307933154

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