Abstract
We study the asymptotic behavior of maximal surfaces like bands and tubes in a neighborhood of an isolated singular point. In particular, we prove possibility of expansion of the radius vector of a two-dimensional surface in a power series with real-analytic coefficients in the time coordinate. We show also that the tangent rays at a singular point constitute a light-like surface. We prove an exact estimate for the existence time for multidimensional maximal tubes in terms of their asymptotic behavior at a singular point and describe completely the class of surfaces on which this estimate is attained.
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Klyachin, V.A. On Asymptotic Properties of Maximal Tubes and Bands in a Neighborhood of an Isolated Singularity in Minkowski Space. Siberian Mathematical Journal 43, 56–67 (2001). https://doi.org/10.1023/A:1013872521000
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DOI: https://doi.org/10.1023/A:1013872521000