Add to ORKGIn this paper we prove the scalar curvature extremality and rigidity for a class of warped product spaces that are possibly degenerate at the two ends. The leaves of these warped product spaces can be any closed Riemannian manifolds with nonnegative curvature operators and nonvanishing Euler characteristics, flat tori, round spheres and their direct products. In particular, we obtain the scalar curvature extremality and rigidity for certain degenerate toric bands and also for round spheres with two antipodal points removed. This answers positively the corresponding questions of Gromov in all dimensions.Comment: 36 pages. v2 contains some minor reorganizations and revision
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COLARES, Antônio Gervásio ; LIMA, Henrique Fernandes de. Some rigidity theorems in semi-Riemannian w...
We consider the curvature of a family of warped products of two pseduo-Riemannian manifolds (B, gB) ...
In this paper we study the space of solutions to an overdetermined linear system involving the Hessi...
We study the structure of Sobolev spaces on the cartesian/warped products of a given metric measure ...
Gromov and Sormani conjectured that a sequence of three dimensional Riemannian manifolds with nonneg...
In this paper we study warped product Einstein metrics over spaces with constant scalar curvature. W...
Gromov and Sormani conjectured that sequences of compact Riemannian manifolds with nonnegative scala...
In a recent study [D.D,], F.Dobarro and E. L. Dozo have studied from the viewpoint of patial deffere...
In this paper we study warped product Einstein metrics over spaces with constant scalar curvature. W...
AbstractIn this paper we study geodesic completeness of Riemannian doubly warped products and Lorent...
Following Gromov, a Riemannian manifold is called area-extremal if any modification that increases s...
In this paper we prove two inequalities relating the warping function to various curvature terms, fo...
By using Gromov's $\mu$-bubble technique, we show that the $3$-dimensional spherical caps are rigid ...
AbstractWe give a Riccati type formula adapted for two metrics having the same geodesics rays starti...
We describe the local structure of Riemannian manifolds with harmonic curvature which admit a maximu...
COLARES, Antônio Gervásio ; LIMA, Henrique Fernandes de. Some rigidity theorems in semi-Riemannian w...
We consider the curvature of a family of warped products of two pseduo-Riemannian manifolds (B, gB) ...
In this paper we study the space of solutions to an overdetermined linear system involving the Hessi...
We study the structure of Sobolev spaces on the cartesian/warped products of a given metric measure ...