Conjugate plateau constructions in product spaces

DOI10.1007/978-3-031-39916-9_3arXiv2203.13162OpenAlexW4387758200MaRDI QIDQ6120643

José M. Manzano, Jesús Castro-Infantes, Francisco Torralbo

Publication date: 25 March 2024

Published in: New Trends in Geometric Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2203.13162

zbMATH Keywords

minimal surfacesconstant mean curvature surfacesDaniel's conjugationhomogeneous product spaces

Mathematics Subject Classification ID

Minimal surfaces in differential geometry, surfaces with prescribed mean curvature (53A10) Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42)

Cites Work

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• Compact embedded minimal surfaces in \(\mathbb{S}^2 \times \mathbb{S}^1\)
• On doubly periodic minimal surfaces in \(\mathbb H^2 \times\mathbb R\) with finite total curvature in the quotient space
• Minimal surfaces with positive genus and finite total curvature in \(\mathbb{H}^2 \times \mathbb{R}\)
• On the classification of Killing submersions and their isometries
• Periodic constant mean curvature surfaces in \(\mathbb{H}^2 \times \mathbb{R}\)
• Complete constant mean curvature surfaces in homogeneous spaces
• A Hopf differential for constant mean curvature surfaces in \(\mathbb S^2 \times \mathbb R\) and \(\mathbb H^2 \times\mathbb R\)
• Construction of harmonic diffeomorphisms and minimal graphs
• New complete embedded minimal surfaces in \({\mathbb {H} ^2\times \mathbb {R}}\)
• Minimal surfaces in \(\widehat PSL_2(\mathbb R)\)
• Dual quadratic differentials and entire minimal graphs in Heisenberg space
• Helicoidal minimal surfaces of prescribed genus
• Compact minimal surfaces in the Berger spheres
• Compact constant mean curvature surfaces in Euclidean three-space
• Isometric immersions into 3-dimensional homogeneous manifolds
• Associate and conjugate minimal immersions in \(M \times R\)
• General curvature estimates for stable H-surfaces in 3-manifolds applications
• Rotationally invariant constant mean curvature surfaces in homogeneous 3-manifolds
• The Bonnet problem for surfaces in homogeneous 3-manifolds
• On complete mean curvature \(\frac 12\) surfaces in \(\mathbb{H}^2\times\mathbb{R}\)
• Height estimates for surfaces with positive constant mean curvature in \(\mathbb M^2\times\mathbb R\)
• Totally umbilic surfaces in homogeneous 3-manifolds
• The topology of complete minimal surfaces of finite total Gaussian curvature
• Cut locus of the B-spheres
• The space of minimal embeddings of a surface into a three-dimensional manifold of positive Ricci curvature
• On the behavior of a non-parametric minimal surface in a non-convex quadrilateral
• New minimal surfaces in S 3
• Embedded minimal surfaces derived from Scherk's examples
• The existence of embedded minimal surfaces and the problem of uniqueness
• The classical Plateau problem and the topology of three-dimensional manifolds. The embedding of the solution given by Douglas-Morrey and an analytic proof of Dehn's lemma
• The triply periodic minimal surfaces of Alan Schoen and their constant mean curvature companions
• Weierstrass type representation of harmonic maps into symmetric spaces
• New surfaces of constant mean curvature
• Minimal surfaces in \(M^2\times \mathbb{R}\)
• Minimal surfaces in \(\mathbb{H}^2\times\mathbb{R}\).
• Mean curvature one surfaces in hyperbolic space, and their relationship to minimal surfaces in Euclidean space
• Minimal surfaces in the round three-sphere by doubling the equatorial two-sphere. I
• On the characterization of minimal surfaces with finite total curvature in \({\mathbb {H}}^2\times {\mathbb {R}}\) and \(\widetilde{\mathrm{PSL}}_2 ({\mathbb {R}})\)
• Height and area estimates for constant mean curvature graphs in \(\mathbb {E}(\kappa ,\tau )\)-spaces
• The gyroid is embedded and has constant mean curvature companions
• On the uniqueness of isoperimetric solutions and imbedded soap bubbles in non-compact symmetric spaces. I
• On the classification of constant mean curvature tori
• Constant mean curvature surfaces constructed by fusing Wente tori
• Minimal graphs in \(\widetilde{\mathrm{PSL}_2(\mathbb R)}\) over unbounded domains
• The Gauss map of surfaces in \(\widetilde{\mathrm {PSL}}_2(\mathbb R)\)
• Constant mean curvature surfaces based on fundamental quadrilaterals
• On the asymptotic plateau problem in \(\widetilde{\mathrm{SL}}_2 (\mathbb{R})\)
• Horizontal Delaunay surfaces with constant mean curvature in \(\mathbb{S}^2 \times \mathbb{R}\) and \(\mathbb{H}^2 \times \mathbb{R} \)
• New examples of constant mean curvature surfaces in \(\mathbb S^2 \times \mathbb R\) and \(\mathbb H^2 \times \mathbb R\)
• On complete constant mean curvature vertical multigraphs in \(\mathbb E(\kappa,\tau)\)
• The reflection principle for minimal submanifolds of Riemannian symmetric spaces
• Harmonic maps from a 2-torus to the 3-sphere
• Classical Schwarz reflection principle for Jenkins-Serrin type minimal surfaces
• Embedded constant mean curvature tori in the three-sphere
• Constant mean curvature \(k\)-noids in homogeneous manifolds
• A Schoen theorem for minimal surfaces in \(\mathbb{H}^2 \times \mathbb{R}\)
• Compact stable surfaces with constant mean curvature in Killing submersions
• Estimates for constant mean curvature graphs in \(M\times\mathbb{R}\)
• Remarks relevant to minimal surfaces and to surfaces of prescribed mean curvature
• Complete minimal surfaces in \(S^ 3\)
• A characterization of constant mean curvature surfaces in homogeneous 3-manifolds
• Non-simply connected minimal planar domains in $\mathbb {H}^2\times \mathbb {R}$
• Minimal surfaces with limit ends in
• The Dirichlet problem for the minimal surface equation, with possible infinite boundary data, over domains in a Riemannian surface
• Construction of triply periodic minimal surfaces
• Survey of local properties of solutions of elliptic partial differential equations
• PARABOLIC AND HYPERBOLIC SCREW MOTION SURFACES IN ℍ²×ℝ
• Minimal surfaces in the three-sphere by doubling the Clifford torus
• Half-space theorem, embedded minimal annuli and minimal graphs in the Heisenberg group
• Holomorphic quadratic differentials and the Bernstein problem in Heisenberg space
• Computing Discrete Minimal Surfaces and Their Conjugates
• Gyroids of Constant Mean Curvature
• Triunduloids: embedded constant mean curvature surfaces with three ends and genus zero
• INVARIANT CMC SURFACES IN ${\mathbb H}^2\times {\mathbb R}$
• Constant mean curvature surfaces in metric Lie groups
• Isoperimetric domains in the Riemannian product of a circle with a simply connected space form and applications to free boundary problems
• Isoparametric surfaces in $E(\kappa,\tau)$-spaces
• A Construction of Constant Mean Curvature Surfaces in ℍ2 × ℝ and the Krust Property
• Compact embedded surfaces with constant mean curvature in $\Bbb{S}^2\times\Bbb{R}$
• Deformations of Symmetric CMC Surfaces in the 3-Sphere
• The Surface Evolver
• Minimizing the Squared Mean Curvature Integral for Surfaces in Space Forms
• Saddle towers and minimal k-noids in ℍ² × ℝ
• On stable compact minimal submanifolds
• AN ELEMENTARY PROOF OF THE ABRESCH ROSENBERG THEOREM ON CONSTANT MEAN CURVATURE IMMERSED SURFACES IN S2 x R AND H2 x R
• The Plateau problem at infinity for horizontal ends and genus 1
• Constant mean curvature isometric immersions into \(\mathbb{S}^2\times\mathbb{R}\) and \(\mathbb{H}^2\times\mathbb{R}\) and related results
• GENUS MINIMAL k-NOIDS AND SADDLE TOWERS IN

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