90 citations · 328 across the 25 of their papers we have counts for
26 papers · 1 filter
A short proof of Bernstein's theorem via the Omori--Yau maximum principle
Luis J. Alias, Miguel A. Meroño
We give a short, self-contained proof of Bernstein's theorem: every entire minimal graph in is a plane. The only global tool is the Omori-Yau maximum principle, which holds o…
A maximum principle related to volume growth and applications
Luis J. Alias, Antonio Caminha, F. Yure do Nascimento
In this paper, we derive a new form of maximum principle for smooth functions on a complete noncompact Riemannian manifold for which there exists a bounded vector field suc…
Mean curvature flow solitons in the presence of conformal vector fields
Luis Alías, Jorge H. de Lira, Marco Rigoli
The aim of this paper is to introduce a notion of mean curvature flow soliton general enough to encompass target spaces of constant sectional curvature, Riemannian products or, in…
On the first stability eigenvalue of constant mean curvature surfaces into homogeneous 3-manifolds
Luis J. Alías, Miguel A. Meroño, Irene Ortiz
We find out upper bounds for the first eigenvalue of the stability operator for compact constant mean curvature surfaces immersed into certain 3-dimensional Riemannian spaces, in p…
A general form of the weak maximum principle and some applications
Guglielmo Albanese, Luis J. Alias, Marco Rigoli
The aim of this paper is to introduce new forms of the weak and Omori-Yau maximum principles for linear operators, notably for trace type operators, and show their usefulness, for…
Higher order mean curvature estimates for bounded complete hypersurfaces
L. J. Alias, M. Dajczer, M. Rigoli
We obtain sharp estimates involving the mean curvatures of higher order of a complete bounded hypersurface immersed in a complete Riemannian manifold. Similar results are also give…