A note on Killing fields and CMC hypersurfaces

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:431

Article

Mari, L.¹  Mastrolia, P.²  Rigoli, M.^1,2 

[1] Univ Fed Ceara, Dept Matemat, Fortaleza, Ceara, Brazil

[2] Univ Milan, Dipartimento Matemat, I-20122 Milan, Italy

关键词: Killing vector field;    Hypersurface;    Mean curvature;    Stability;    Oscillation;   

DOI  :  10.1016/j.jmaa.2015.06.016

来源: Elsevier

【 摘 要 】

In this note we give some sufficient conditions for a CMC-hypersurface in a Riemannian manifold N to be invariant under the 1-parameter group of isometries generated by a Killing field on N. Our main result improves on previous ones by D. Hoffman, R. Osserman, and R. Schoen and S. Fornari and J. Ripoll, and hinges on a new, simple existence theorem for a first zero of solutions of an ODE naturally associated to the problem. This theorem implies some classical oscillation criteria of W. Ambrose and R. Moore. Extension to constant higher-order mean curvature hypersurfaces are also presented. (C) 2015 Elsevier Inc. All rights reserved.

【 授权许可】

Free