# Duality of boundary value problems for minimal and maximal surfaces

@article{Akamine2019DualityOB, title={Duality of boundary value problems for minimal and maximal surfaces}, author={Shintaro Akamine and Hiroki Fujino}, journal={arXiv: Differential Geometry}, year={2019} }

In 1966, Jenkins and Serrin gave existence and uniqueness results for infinite boundary value problems of minimal surfaces in the Euclidean space, and after that such solutions have been studied by using the univalent harmonic mapping theory. In this paper, we show that there exists a one-to-one correspondence between solutions of infinite boundary value problems for minimal surfaces and those of lightlike line boundary problems for maximal surfaces in the Lorentz-Minkowski spacetime. We also…

## 3 Citations

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As in the case of minimal surfaces in the Euclidean 3-space, the reflection principle for maximal surfaces in the Lorentz-Minkowski 3-space asserts that if a maximal surface has a spacelike line…

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In the minimal surface theory, the Krust theorem asserts that if a minimal surface in the Euclidean 3-space E is the graph of a function over a convex domain, then each surface of its associated…

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Consider the Lorentz-Minkowski $3$-space $\mathbb{L}^3$ with the metric $dx^2+dy^2-dz^2$ in canonical coordinates $(x,y,z)$. A surface in $\mathbb{L}^3$ is said to be separable if satisfies an…

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