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The Symmetric Minimal Surface Equation [PDF]
Indiana University Mathematics Journal, 2023 and, geometrically, A (u) represents the area functional for S(u); that is, A (u) is the (n+m−1)-dimensional Hausdorff measure H n+m−1(S(u)). This is clear because the integrand √ 1+|Du|2 um−1 for A (u) is the Jacobian of the map (x,ω) ∈Ω×Sm−1 7→ (x, u(x)
Kaveh Fouladgar, Leon Simon
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Symmetric solutions of the singular minimal surface equation [PDF]
Annals of Global Analysis and Geometry, 2021 We classify all rotational symmetric solutions of the singular minimal surface equation in both cases α0$$\end{document}. In addition, we discuss further geometric and analytic properties of the solutions, in particular stability, minimizing properties ...
Ulrich Dierkes, Nico Groh
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An Inverse Problem for the Riemannian Minimal Surface Equation
Journal of Differential Equations, 2023 In this paper we consider determining a minimal surface embedded in a Riemannian manifold $ \times \mathbb{R}$. We show that if $ $ is a two dimensional Riemannian manifold with boundary, then the knowledge of the associated Dirichlet-to-Neumann map for the minimal surface equation determine $ $ up to an isometry.
Cătălin I. Cârstea +3 more
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Algebraic Aspects of the Supersymmetric Minimal Surface Equation [PDF]
Symmetry, 2017 In this paper, a supersymmetric extension of the minimal surface equation is formulated. Based on this formulation, a Lie superalgebra of infinitesimal symmetries of this equation is determined.
A. M. Grundland, A. J. Hariton
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A duality result between the minimal surface equation and the maximal surface equation [PDF]
Anais da Academia Brasileira de Ciências, 2001 In this note we show how classical Bernstein's theorem on minimal surfaces in the Euclidean space can be seen as a consequence of Calabi-Bernstein's theorem on maximal surfaces in the Lorentz-Minkowski space (and viceversa).
ALÍAS LUIS J., PALMER BENNETT
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Numerical solution of the minimal surface equation [PDF]
Mathematics of Computation, 1967 Paul Concus
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The time-like minimal surface equation in Minkowski space: low regularity solutions [PDF]
Inventiones Mathematicae, 2021 It has long been conjectured that for nonlinear wave equations that satisfy a nonlinear form of the null condition, the low regularity well-posedness theory can be significantly improved compared to the sharp results of Smith-Tataru for the generic case.
Albert Ai, Mihaela Ifrim, Daniel Tataru
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An inverse problem for the minimal surface equation [PDF]
Nonlinear Analysis, 2022 22 pages, Modified assumptions in Theorem 1.1 and added partial data results, changed the proof accordingly, removed Propositions 5.2 and 5.3 for being redundant in this modified case of the main theorem, corrected ...
J. Nurminen
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An inverse problem for the minimal surface equation in the presence of a riemannian metric [PDF]
Nonlinearity, 2023 In this work we study an inverse problem for the minimal surface equation on a Riemannian manifold (Rn,g) where the metric is of the form g(x)=c(x)(g^⊕e) .
Janne Nurminen
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Bifurcation for minimal surface equation in hyperbolic 3-manifolds [PDF]
Annales de l'Institut Henri Poincaré C, Analyse non linéaire, 2019 Initiated by the work of Uhlenbeck in late 1970s, we study existence, multiplicity and asymptotic behavior for minimal immersions of a closed surface in some hyperbolic three-manifold, with prescribed conformal structure on the surface and second fundamental form of the immersion.
Zheng Huang +2 more
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