Dirichlet boundary values on Euclidean balls with infinitely many solutions for the minimal surface system

DOI10.1016/j.matpur.2019.01.019zbMath1425.53011arXiv1905.08532OpenAlexW2914663400WikidataQ128547510 ScholiaQ128547510MaRDI QIDQ2274024

Yanyan Li

Publication date: 19 September 2019

Published in: Journal de Mathématiques Pures et Appliquées. Neuvième Série (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1905.08532

zbMATH Keywords

singular solutionsanalytic solutionsdynamic systemDirichlet problem for minimal surface systemLawson-Osserman constructions

Mathematics Subject Classification ID

Higher-dimensional and -codimensional surfaces in Euclidean and related (n)-spaces (53A07) Minimal surfaces in differential geometry, surfaces with prescribed mean curvature (53A10) Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42) Harmonic maps, etc. (58E20)

Related Items

Higher codimension minimal submanifold with isolated singularity, Existence and non-existence of minimal graphs, Self-expanders to the mean curvature flow based on the generalized Lawson-Osserman cone, Minimal submanifolds of higher codimension, A Bernstein-type theorem for minimal graphs of higher codimension via singular values

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• The Gauss image of entire graphs of higher codimension and Bernstein type theorems
• Multiple solutions for the nonparametric Plateau problem within the Euclidean space \(\mathbb R^p\) of arbitrary dimension
• Convex functions on Grassmannian manifolds and Lawson-Osserman problem
• Calibrated geometries
• Minimal immersions of projective spaces into spheres
• An extrinsic rigidity theorem for minimal immersions from \(S^2\) into \(S^n\)
• Degree of the standard isometric minimal immersions of complex projective spaces into spheres
• Some rigidity theorems for minimal submanifolds of the sphere
• Degree of the standard isometric minimal immersions of the symmetric spaces of rank one into spheres
• Non-existence, non-uniqueness and irregularity of solutions to the minimal surface system
• New area-minimizing Lawson-Osserman cones
• On realization of tangent cones of homologically area-minimizing compact singular submanifolds
• Submanifolds with constant Jordan angles and rigidity of the Lawson-Osserman cone
• A spherical Bernstein theorem for minimal submanifolds of higher codimension
• The low-dimensional metric foliations of Euclidean spheres
• Geometric measure theory.
• Geometry of harmonic maps
• Bernstein type theorems for higher codimension
• Minimal immersions of Riemannian manifolds
• Minimal immersions of surfaces in Euclidean spheres
• Una maggiorazione a priori relativa alle ipersuperfici minimali non parametriche
• Minimal immersions of spheres into spheres
• Le spectre d'une variété riemannienne. (The spectrum of a Riemannian manifold)
• The Geometry of Grassmannian manifolds and Bernstein type theorems for higher codimension
• Harmonic Maps and Minimal Immersions with Symmetries (AM-130)
• Heat Equations on Minimal Submanifolds and Their Applications
• Eigenmaps and the space of minimal immersions between spheres
• A new proof of de Giorgi's theorem concerning the regularity problem for elliptic differential equations
• DIFFERENTIAL GEOMETRY OF GRASSMANN MANIFOLDS
• The Dirichlet problem for the minimal surface equation in higher dimensions.
• Higher Torsion in H-Spaces
• Index parity of closed geodesics and rigidity of Hopf fibrations
• Conformal geometry of surfaces in \(S^4\) and quaternions