Year: 2021
Type: preprint
Abstract: In this article, we use the inverse function theorem for Banach spaces to interpolate a given real analytic spacelike curve $a$ in Lorentz-Minkowski space $\mathbb{L}^3$ to another real analytic spacelike curve $c$, which is ``close" enough to $a$ in a certain sense by constructing a maximal surface containing them. Next we apply the same method to interpolate two given real analytic curve $a$ in Euclidean space $\mathbb{E}^3$ and a real analytic curve $c$, which is also ``close" enough to ``a" in a certain sense with a minimal surface. Throughout this study, the Björling problem and Schwarz's solution to it play pivotal roles.
Source: arXiv (Cornell University)
Authors: Dey, Rukmini, Singh, Rahul Kumar
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4386301622