47 research outputs found
On the manifold structure of the set of unparameterized embeddings with low regularity
Given manifolds and , with compact, we study the geometrical
structure of the space of embeddings of into , having less regularity
than , quotiented by the group of diffeomorphisms of .Comment: To appear in the Bulletin of the Brazilian Mathematical Societ
Hypersurfaces of constant higher order mean curvature in warped products
In this paper we characterize compact and complete hypersurfaces with some
constant higher order mean curvature into warped product spaces. Our approach
is based on the use of a new trace operator version of the Omori-Yau maximum
principle which seems to be interesting in its own.Comment: To appear in the Transactions of the American Mathematical Society.
See http://www.ams.org/cgi-bin/mstrack/accepted_papers?jrnl=tra
On the scalar curvature of constant mean curvature hypersurfaces in space forms
In this paper we study the behavior of the scalar curvature of a complete
hypersurface immersed with constant mean curvature into a Riemannian space form
of constant curvature, deriving a sharp estimate for the infimum of . Our
results will be an application of a weak Omori-Yau maximum principle due to
Pigola, Rigoli and Setti \cite{PRS}.Comment: Final version (August 2009). To appear in Journal of Mathematical
Analysis and Applications. Dedicated to Professor Marcos Dajczer on the
occasion of his 60th birthda
Geometric analysis of Lorentzian distance function on spacelike hypersurfaces
Some analysis on the Lorentzian distance in a spacetime with controlled
sectional (or Ricci) curvatures is done. In particular, we focus on the study
of the restriction of such distance to a spacelike hypersurface satisfying the
Omori-Yau maximum principle. As a consequence, and under appropriate hypotheses
on the (sectional or Ricci) curvatures of the ambient spacetime, we obtain
sharp estimates for the mean curvature of those hypersurfaces. Moreover, we
also give a suficient condition for its hyperbolicity.Comment: Final version (January 2009). To appear in the Transactions of the
American Mathematical Societ