NEW COMPLEX ANALYTIC METHODS IN THE THEORY OF MINIMAL SURFACES: A SURVEY

DOI10.1017/S1446788718000125zbMath1414.53007arXiv1711.08024WikidataQ129342394 ScholiaQ129342394MaRDI QIDQ5379025

Antonio Alarcón, Franc Forstnerič

Publication date: 27 May 2019

Published in: Journal of the Australian Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1711.08024

zbMATH Keywords

minimal surfaceRiemann surfaceOka manifold

Mathematics Subject Classification ID

Minimal surfaces in differential geometry, surfaces with prescribed mean curvature (53A10) Research exposition (monographs, survey articles) pertaining to differential geometry (53-02)

Related Items (15)

Holomorphic Legendrian curves in projectivised cotangent bundles ⋮ Approximation theorems for Pascali systems ⋮ Evolution of form and shape ⋮ Recent developments on Oka manifolds ⋮ Domains without parabolic minimal submanifolds and weakly hyperbolic domains ⋮ A foliation of the ball by complete holomorphic discs ⋮ Proper superminimal surfaces of given conformal types in the hyperbolic four-space ⋮ Legendrian curves in \(\mathbb{C} P^3\): cubics and curves on a quadric surface ⋮ Holomorphic Approximation: The Legacy of Weierstrass, Runge, Oka–Weil, and Mergelyan ⋮ Interpolation and optimal hitting for complete minimal surfaces with finite total curvature ⋮ The Calabi-Yau property of superminimal surfaces in self-dual Einstein four-manifolds ⋮ Interpolation by complete minimal surfaces whose Gauss map misses two points ⋮ Carleman approximation by conformal minimal immersions and directed holomorphic curves ⋮ The Calabi-Yau problem for Riemann surfaces with finite genus and countably many ends ⋮ Holomorphic Legendrian curves in \(\mathbb{CP}^3\) and superminimal surfaces in \(\mathbb{S}^4\)

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