oalib
Search Results: 1 - 10 of 100 matches for " "
All listed articles are free for downloading (OA Articles)
Page 1 /100
Display every page Item
Stable hypersurfaces with zero scalar curvature in Euclidean space  [PDF]
Hilário Alencar,Manfredo do Carmo,Gregório Silva Neto
Mathematics , 2015,
Abstract: In this paper we prove some results concerning stability of hypersurfaces in the four dimensional Euclidean space with zero scalar curvature. First we prove there is no complete stable hypersurface with zero scalar curvature, polynomial growth of integral of the mean curvature, and with the Gauss-Kronecker curvature bounded away from zero. We conclude this paper giving a sufficient condition for a regular domain to be stable in terms of the mean and the Gauss-Kronecker curvatures of the hypersurface and the extrinsic diameter of the domain.
Stable hypersurfaces with constant scalar curvature in Euclidean spaces  [PDF]
Hilário Alencar,Walcy Santos,Detang Zhou
Mathematics , 2009,
Abstract: We obtain some nonexistence results for complete noncompact stable hyppersurfaces with nonnegative constant scalar curvature in Euclidean spaces. As a special case we prove that there is no complete noncompact strongly stable hypersurface $M$ in $\mathbb{R}^{4}$ with zero scalar curvature $S_2$, nonzero Gauss-Kronecker curvature and finite total curvature (i.e. $\int_M|A|^3<+\infty$).
Stable minimal hypersurfaces in a Riemannian manifold with pinched negative sectional curvature  [PDF]
Nguyen Thac Dung,Keomkyo Seo
Mathematics , 2011,
Abstract: We give an estimate of the first eigenvalue of the Laplace operator on a complete noncompact stable minimal hypersurface $M$ in a complete simply connected Riemannian manifold with pinched negative sectional curvature. In the same ambient space, we prove that if a complete minimal hypersurface $M$ has sufficiently small total scalar curvature then $M$ has only one end. We also obtain a vanishing theorem for $L^2$ harmonic 1-forms on minimal hypersurfaces in a Riemannian manifold with sectional curvature bounded below by a negative constant. Moreover we provide sufficient conditions for a minimal hypersurface in a Riemannian manifold with nonpositive sectional curvature to be stable.
Positive scalar curvature and minimal hypersurfaces  [PDF]
Harish Seshadri
Mathematics , 2003,
Abstract: We show that the minimal hypersurface method of Schoen and Yau can be used for the ``quantitative'' study of positive scalar curvature. More precisely, we show that if a manifold admits a metric $g$ with $s_g \ge | T |$ or $s_g \ge | W |$, where $s_g$ is the scalar curvature of of $g$, $T$ any 2-tensor on $M$ and $W$ the Weyl tensor of $g$, then any closed orientable stable minimal (totally geodesic in the second case) hypersurface also admits a metric with the corresponding positivity of scalar curvature. A corollary about the topology of such hypersurfaces is proved in a special situation.
Hypersurfaces with nonnegative scalar curvature  [PDF]
Lan-Hsuan Huang,Damin Wu
Mathematics , 2011,
Abstract: We show that closed hypersurfaces in Euclidean space with nonnegative scalar curvature are weakly mean convex. In contrast, the statement is no longer true if the scalar curvature is replaced by the k-th mean curvature, for k greater than 2, as we construct the counter-examples for all k greater than 2. Our proof relies on a new geometric inequality which relates the scalar curvature and mean curvature of a hypersurface to the mean curvature of the level sets of a height function. By extending the argument, we show that complete non-compact hypersurfaces of finitely many regular ends with nonnegative scalar curvature are weakly mean convex, and prove a positive mass theorem for such hypersurfaces.
Complete minimal hypersurfaces in the hyperbolic space $\mathbb{H}^4$ with vanishing Gauss-Kronecker curvature  [PDF]
T. Hasanis,A. Savas-Halilaj,T. Vlachos
Mathematics , 2005,
Abstract: We investigate 3-dimensional complete minimal hypersurfaces in the hyperbolic space $\mathbb{H}^{4}$ with Gauss-Kronecker curvature identically zero. More precisely, we give a classification of complete minimal hypersurfaces with Gauss-Kronecker curvature identically zero, nowhere vanishing second fundamental form and scalar curvature bounded from below.
Hypersurfaces of prescribed scalar curvature in Lorentzian manifolds  [PDF]
Claus Gerhardt
Mathematics , 2002,
Abstract: The existence of closed hypersurfaces of prescribed scalar curvature in globally hyperbolic Lorentzian manifolds is proved provided there are barriers.
Maximum principles for hypersurfaces with vanishing curvature functions in an arbitrary Riemannian manifold
FONTENELE, FRANCISCO X.;SILVA, SéRGIO L.;
Anais da Academia Brasileira de Ciências , 2002, DOI: 10.1590/S0001-37652002000200002
Abstract: in this paper we generalize and extend to any riemannian manifold maximum principles for euclidean hypersurfaces with vanishing curvature functions obtained by hounie-leite.
Maximum principles for hypersurfaces with vanishing curvature functions in an arbitrary Riemannian manifold  [cached]
FONTENELE FRANCISCO X.,SILVA SéRGIO L.
Anais da Academia Brasileira de Ciências , 2002,
Abstract: In this paper we generalize and extend to any Riemannian manifold maximum principles for Euclidean hypersurfaces with vanishing curvature functions obtained by Hounie-Leite.
Entire scalar curvature flow and hypersurfaces of constant scalar curvature in Minkowski space  [PDF]
Pierre Bayard
Mathematics , 2008,
Abstract: We prove existence in the Minkowski space of entire spacelike hypersurfaces with constant negative scalar curvature and given set of lightlike directions at infinity; we also construct the entire scalar curvature flow with prescribed set of lightlike directions at infinity, and prove that the flow converges to a spacelike hypersurface with constant scalar curvature. The proofs rely on barriers construction and a priori estimates.
Page 1 /100
Display every page Item


Home
Copyright © 2008-2017 Open Access Library. All rights reserved.