scholarly journals Uniqueness of Complete Hypersurfaces in Weighted Riemannian Warped Products

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Ning Zhang
Keyword(s):  
Universal Covering ◽  
Warped Products ◽  
Bernstein Type ◽  
Weighted Mean ◽  
Weak Maximum Principle ◽  
Uniqueness Results ◽  
Weighted Mean Curvature ◽  
Entire Graphs ◽  
Special Case ◽  
Complete Hypersurfaces

In this paper, applying the weak maximum principle, we obtain the uniqueness results for the hypersurfaces under suitable geometric restrictions on the weighted mean curvature immersed in a weighted Riemannian warped product I × ρ M f n whose fiber M has f -parabolic universal covering. Furthermore, applications to the weighted hyperbolic space are given. In particular, we also study the special case when the ambient space is weighted product space and provide some results by Bochner’s formula. As a consequence of this parametric study, we also establish Bernstein-type properties of the entire graphs in weighted Riemannian warped products.

scholarly journals New Bernstein Type Results in Weighted Warped Products

2021 ◽  
Vol 2021 ◽  
pp. 1-6
Author(s):  
Ning Zhang
Keyword(s):  
Mean Curvature ◽  
Constant Mean Curvature ◽  
Warped Products ◽  
Bernstein Type ◽  
Weighted Mean ◽  
Curvature Equation ◽  
Uniqueness Results ◽  
Mean Curvature Equation ◽  
Weighted Mean Curvature ◽  
Entire Graphs

In this paper, we obtain new parametric uniqueness results for complete constant weighted mean curvature hypersurfaces under suitable geometric assumptions in weighted warped products. Furthermore, we also prove very general Bernstein type results for the constant mean curvature equation for entire graphs in these ambient spaces.

scholarly journals UNIQUENESS OF COMPLETE HYPERSURFACES WITH BOUNDED HIGHER ORDER MEAN CURVATURES IN SEMI-RIEMANNIAN WARPED PRODUCTS

2011 ◽  
Vol 54 (1) ◽  
pp. 201-212 ◽  
Author(s):  
C. P. AQUINO ◽  
H. F. DE LIMA
Keyword(s):  
Steady State ◽  
Maximum Principle ◽  
Higher Order ◽  
Hyperbolic Type ◽  
Warped Products ◽  
Higher Order Mean Curvatures ◽  
Uniqueness Results ◽  
State Type ◽  
Type Spaces ◽  
Complete Hypersurfaces

AbstractIn this paper, we deal with complete hypersurfaces immersed with bounded higher order mean curvatures in steady state-type spacetimes and in hyperbolic-type spaces. By applying a generalised maximum principle for the Yau's square operator [11], we obtain uniqueness results in each of these ambient spaces.

Rigidity of entire graphs in weighted product spaces with nonnegative Bakry–Émery–Ricci tensor

2017 ◽  
Vol 17 (1) ◽  
Author(s):  
Henrique F. de Lima ◽  
Arlandson M. S. Oliveira ◽  
Márcio S. Santos
Keyword(s):  
Smooth Function ◽  
Mean Curvature ◽  
Ricci Tensor ◽  
Product Space ◽  
Product Spaces ◽  
Weighted Mean ◽  
Weighted Mean Curvature ◽  
Entire Graphs

AbstractWe study the rigidity of entire graphs defined over the fiber of a weighted product space whose Bakry–Émery–Ricci tensor is nonnegative. Supposing that the weighted mean curvature is constant and assuming appropriated constraints on the norm of the gradient of the smooth function

scholarly journals Spacelike Hypersurfaces in Weighted Generalized Robertson-Walker Space-Times

2018 ◽  
Vol 2018 ◽  
pp. 1-6
Author(s):  
Ximin Liu ◽  
Ning Zhang
Keyword(s):  
Maximum Principle ◽  
Space Time ◽  
Ambient Space ◽  
Weak Maximum Principle ◽  
Uniqueness Results ◽  
Spacelike Hypersurfaces ◽  
Generalized Maximum Principle ◽  
Special Case

Applying generalized maximum principle and weak maximum principle, we obtain several uniqueness results for spacelike hypersurfaces immersed in a weighted generalized Robertson-Walker (GRW) space-time under suitable geometric assumptions. Furthermore, we also study the special case when the ambient space is static and provide some results by using Bochner’s formula.

scholarly journals Space-like hypersurfaces with functionally bounded mean curvature in Lorentzian warped products and generalized Calabi–Bernstein-type problems

2018 ◽  
Vol 149 (04) ◽  
pp. 849-868
Author(s):  
Juan A. Aledo ◽  
Rafael M. Rubio ◽  
Juan J. Salamanca
Keyword(s):  
Riemannian Manifold ◽  
Mean Curvature ◽  
Universal Covering ◽  
Complete Riemannian Manifold ◽  
Warped Products ◽  
Bernstein Type ◽  
Rigidity Results

We study space-like hypersurfaces with functionally bounded mean curvature in Lorentzian warped products , where F is a (non-compact) complete Riemannian manifold whose universal covering is parabolic. In particular, we provide several rigidity results under appropriate mathematical and physical assumptions. As an application, several Calabi–Bernstein-type results are obtained which widely extend the previous ones in this setting.

On Bernstein-type properties of complete hypersurfaces in weighted warped products

2014 ◽  
Vol 195 (2) ◽  
pp. 309-322 ◽  
Author(s):  
Marcos P. Cavalcante ◽  
Henrique F. de Lima ◽  
Márcio S. Santos
Keyword(s):  
Warped Products ◽  
Bernstein Type ◽  
Complete Hypersurfaces

scholarly journals Space-like hypersurfaces with functionally bounded mean curvature in Lorentzian warped products and generalized Calabi–Bernstein-type problems

2018 ◽  
pp. 1-20
Author(s):  
Juan A. Aledo ◽  
Rafael M. Rubio ◽  
Juan J. Salamanca
Keyword(s):  
Riemannian Manifold ◽  
Mean Curvature ◽  
Universal Covering ◽  
Complete Riemannian Manifold ◽  
Warped Products ◽  
Bernstein Type ◽  
Rigidity Results

We study space-like hypersurfaces with functionally bounded mean curvature in Lorentzian warped products , where F is a (non-compact) complete Riemannian manifold whose universal covering is parabolic. In particular, we provide several rigidity results under appropriate mathematical and physical assumptions. As an application, several Calabi–Bernstein-type results are obtained which widely extend the previous ones in this setting.

Bernstein type results for complete spacelike hypersurfaces immersed in a weighted conformally stationary spacetime

2017 ◽  
Vol 28 (10) ◽  
pp. 1750071
Author(s):  
Henrique F. de Lima ◽  
Arlandson M. Oliveira ◽  
Márcio S. Santos ◽  
Marco A. L. Velásquez
Keyword(s):  
Vector Field ◽  
Mean Curvature ◽  
Sufficient Conditions ◽  
Spacelike Hypersurface ◽  
Bernstein Type ◽  
Weighted Mean ◽  
Timelike Vector ◽  
Stationary Spacetime ◽  
Weighted Mean Curvature ◽  
Spacelike Hypersurfaces

In this paper, we deal with complete noncompact spacelike hypersurfaces immersed in a weighted conformally stationary spacetime endowed with a closed conformal timelike vector field [Formula: see text]. Under suitable constraints on the weighted mean curvature of such a spacelike hypersurface, we establish sufficient conditions to ensure that it must be an integral leaf of the foliation orthogonal to [Formula: see text].

UNIQUENESS IN RANDOM-PROPOSER MULTILATERAL BARGAINING

2009 ◽  
Vol 11 (04) ◽  
pp. 407-417 ◽  
Author(s):  
HUIBIN YAN
Keyword(s):  
Subgame Perfect Equilibrium ◽  
Characteristic Functions ◽  
Bargaining Model ◽  
Equilibrium Outcome ◽  
Multilateral Bargaining ◽  
Legislative Bargaining ◽  
Uniqueness Results ◽  
Subgame Perfect Equilibria ◽  
Perfect Equilibria ◽  
Special Case

Solution uniqueness is an important property for a bargaining model. Rubinstein's (1982) seminal 2-person alternating-offer bargaining game has a unique Subgame Perfect Equilibrium outcome. Is it possible to obtain uniqueness results in the much enlarged setting of multilateral bargaining with a characteristic function? This paper investigates a random-proposer model first studied in Okada (1993) in which each period players have equal probabilities of being selected to make a proposal and bargaining ends after one coalition forms. Focusing on transferable utility environments and Stationary Subgame Perfect Equilibria (SSPE), we find ex ante SSPE payoff uniqueness for symmetric and convex characteristic functions, considerably expanding the conditions under which this model is known to exhibit SSPE payoff uniqueness. Our model includes as a special case a variant of the legislative bargaining model in Baron and Ferejohn (1989), and our results imply (unrestricted) SSPE payoff uniqueness in this case.

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