Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 41, 2016, 699-704

A BERNSTEIN PROBLEM IN WARPED PRODUCTS

Juan A. Aledo and Rafael M. Rubio

Universidad de Castilla-La Mancha, Departamento de Matemáticas, E.S.I. Informática
02071 Albacete, Spain; juanangel.aledo 'at' uclm.es

Universidad de Córdoba, Departamento de Matemáticas
Campus de Rabanales, 14071 Córdoba, Spain; rmrubio 'at' uco.es

Abstract. Uniqueness and non-existence of entire solutions to the minimal surface equation in warped products R² ×_f R are provided. As a consequence of our results, the classical Bernstein's Theorem is extended.

2010 Mathematics Subject Classification: Primary 35J60, 58J05.

Key words: Minimal surface equation, Bernstein's theorem, Riemannian warped product.

Reference to this article: J.A. Aledo and R.M. Rubio: A Bernstein problem in warped products. Ann. Acad. Sci. Fenn. Math. 41 (2016), 699-704.

Full document as PDF file

doi:10.5186/aasfm.2016.4139