Bernstein theorems for length and area decreasing minimal maps

DOI10.1007/s00526-013-0646-0zbMath1301.53053arXiv1205.2379OpenAlexW2058762528MaRDI QIDQ2510350

Andreas Savas-Halilaj, Knut Smoczyk

Publication date: 1 August 2014

Published in: Calculus of Variations and Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1205.2379

zbMATH Keywords

Bochner-Weitzenbock formulaBernstein Theoremstrong elliptic maximum principlelength and area decreasing minimal maps

Mathematics Subject Classification ID

Higher-dimensional and -codimensional surfaces in Euclidean and related (n)-spaces (53A07) Elliptic equations on manifolds, general theory (58J05) Global submanifolds (53C40) Second-order elliptic systems (35J47)

Related Items (17)

A Bernstein theorem for minimal maps with small second fundamental form ⋮ Mean convex properly embedded \([ \varphi , \vec{e}_3 \)-minimal surfaces in \(\mathbb{R}^3\)] ⋮ On the topology of translating solitons of the mean curvature flow ⋮ Mean curvature flow of area decreasing maps between Riemann surfaces ⋮ Gauss maps of harmonic and minimal great circle fibrations ⋮ Evolution of area-decreasing maps between two-dimensional Euclidean spaces ⋮ Homotopy of area decreasing maps by mean curvature flow ⋮ Graphical mean curvature flow ⋮ Mean curvature flow of contractions between Euclidean spaces ⋮ The Ricci-Bourguignon flow ⋮ Self-expanders of the mean curvature flow ⋮ A Bernstein-type theorem for minimal graphs of higher codimension via singular values ⋮ Rigidity of the Hopf fibration ⋮ Equilibrium of surfaces in a vertical force field ⋮ A Schwarz-Pick lemma for minimal maps ⋮ Graphical mean curvature flow with bounded bi-Ricci curvature ⋮ Evolution of contractions by mean curvature flow

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