Extension of Krust theorem and deformations of minimal surfaces

DOI10.1007/s10231-022-01211-zOpenAlexW3204046941WikidataQ113904724 ScholiaQ113904724MaRDI QIDQ2088029

Hiroki Fujino, Shintaro Akamine

Publication date: 21 October 2022

Published in: Annali di Matematica Pura ed Applicata. Serie Quarta (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2110.00746

zbMATH Keywords

minimal surfacemaximal surfaceplanar harmonic mappingKrust-type theorem

Mathematics Subject Classification ID

Minimal surfaces in differential geometry, surfaces with prescribed mean curvature (53A10) Harmonic, subharmonic, superharmonic functions in two dimensions (31A05) Local differential geometry of Lorentz metrics, indefinite metrics (53B30) Boundary behavior (theorems of Fatou type, etc.) of harmonic functions in two dimensions (31A20)

Related Items

A version of Krust’s theorem for anisotropic minimal surfaces

Cites Work

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• Maximal surfaces with conelike singularities
• Univalent harmonic mappings and linearly connected domains
• The Lorentzian version of a theorem of Krust
• Weierstrass-type representations
• Extensions of the duality between minimal surfaces and maximal surfaces
• Global geometry and topology of spacelike stationary surfaces in the 4-dimensional Lorentz space
• Maximal surfaces with singularities in Minkowski space
• On embedded complete minimal surfaces of genus zero
• Differentialgeometrie des isotropen Raumes. 3. Flächentheorie
• Holomorphic representation of minimal surfaces in simply isotropic space
• Quasiconformal harmonic mappings and close-to-convex domains
• Injectivity of harmonic mappings with a specified injective holomorphic part
• Minimal Surfaces
• How many maximal surfaces do correspond to one minimal surface?
• Generalized maximal surfaces in Lorentz–Minkowski space L³
• A parametrization of the Weierstrass formulae and perturbation of complete minimal surfaces in R3 into the hyperbolic 3-space.
• Minimal graphs in ℝ³ over convex domains
• Harmonic univalent functions
• $d$-Minimal Surfaces in Three-Dimensional Singular Semi-Euclidean Space $\mathbb{R}^{0,2,1}$
• Maximal surfaces of Riemann type in Lorentz-Minkowski space \(\mathbb L^3\)