Interpolation by maximal and minimal surfaces

Fuente: arXiv
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Auteurs principaux: Dey, Rukmini, Singh, Rahul Kumar
Format: Preprint
Publié: 2021
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author Dey, Rukmini
Singh, Rahul Kumar
author_facet Dey, Rukmini
Singh, Rahul Kumar
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2102_03019
institution arXiv
publishDate 2021
record_format arxiv
spellingShingle Interpolation by maximal and minimal surfaces
Dey, Rukmini
Singh, Rahul Kumar
Differential Geometry
Functional Analysis
53A35, 53B30
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.
title Interpolation by maximal and minimal surfaces
topic Differential Geometry
Functional Analysis
53A35, 53B30
url https://arxiv.org/abs/2102.03019