Bernstein-type theorems in a Riemannian manifold with an irrotational Killing vector field

DOI10.1007/s00009-015-0546-yzbMath1351.58015OpenAlexW1984329404WikidataQ115390390 ScholiaQ115390390MaRDI QIDQ327373

Alfonso Romero, Rafael M. Rubio

Publication date: 19 October 2016

Published in: Mediterranean Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00009-015-0546-y

zbMATH Keywords

compact Riemannian manifoldsKilling vector fieldsnonlinear PDE of divergence formuniqueness of entire solutions

Mathematics Subject Classification ID

Minimal surfaces in differential geometry, surfaces with prescribed mean curvature (53A10) Elliptic equations on manifolds, general theory (58J05) Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42) Entire solutions to PDEs (35B08) Quasilinear elliptic equations with mean curvature operator (35J93)

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Cites Work

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• On the oriented Plateau problem
• Minimal surfaces in \(M^2\times \mathbb{R}\)
• Minimal varieties in Riemannian manifolds
• The theory of minimal surfaces in \(M\times \mathbb R\)
• On S. Bernstein's Theorem on Surfaces z(x, y) of Nonpositive Curvature

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