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

2022/10/31 by Manikoth, Sreedev
#53A10 #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2210.17137

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.

Related

• Interpolation by maximal and minimal surfaces
• Piecewise minimal surfaces interpolating between two real analytic curves
• Björling problem for timelike surfaces in the Lorentz-Minkowski space
• On the Björling problem for Willmore surfaces
• Timelike Minimal Surfaces via Loop Groups