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

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.

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Rigidity of complete hypersurfaces in warped product spaces via higher order mean curvatures

Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry ◽

10.1007/s13366-016-0288-4 ◽

2016 ◽

Vol 57 (2) ◽

pp. 391-405 ◽

Cited By ~ 1

Author(s):

Cícero P. Aquino ◽

Jogli G. Araújo ◽

Henrique F. de Lima

Keyword(s):

Warped Product ◽

Higher Order ◽

Product Spaces ◽

Higher Order Mean Curvatures ◽

Warped Product Spaces ◽

Complete Hypersurfaces

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Uniqueness of Complete Hypersurfaces in Weighted Riemannian Warped Products

Advances in Mathematical Physics ◽

10.1155/2021/3234263 ◽

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.

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Complete spacelike hypersurfaces in a Robertson–Walker spacetime

Mathematical Proceedings of the Cambridge Philosophical Society ◽

10.1017/s0305004111000351 ◽

2011 ◽

Vol 151 (2) ◽

pp. 271-282 ◽

Cited By ~ 20

Author(s):

ALMA L. ALBUJER ◽

FERNANDA E. C. CAMARGO ◽

HENRIQUE F. DE LIMA

Keyword(s):

Maximum Principle ◽

Mean Curvature ◽

Constant Mean Curvature ◽

Rigidity Results ◽

Complete Spacelike Hypersurfaces ◽

Uniqueness Results ◽

Spacelike Hypersurfaces ◽

Generalized Maximum Principle ◽

Non Parametric

AbstractIn this paper, as a suitable application of the well-known generalized maximum principle of Omori–Yau, we obtain uniqueness results concerning to complete spacelike hypersurfaces with constant mean curvature immersed in a Robertson–Walker (RW) spacetime. As an application of such uniqueness results for the case of vertical graphs in a RW spacetime, we also get non-parametric rigidity results.

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Theoretical analysis of RNA polymerase fidelity: a steady-state copolymerization approach

Communications in Theoretical Physics ◽

10.1088/1572-9494/ac3993 ◽

2021 ◽

Author(s):

Wenbo Fu ◽

Qiushi Li ◽

Yongshun Song ◽

Yaogen Shu ◽

Zhongcan Ouyang ◽

...

Keyword(s):

Steady State ◽

Dna Replication ◽

Theoretical Analysis ◽

Rna Polymerase ◽

Higher Order ◽

Simplified Models ◽

Rna Transcription ◽

Dna Transcription ◽

Polymerase Fidelity ◽

Neighbor Effects

Abstract The fidelity of DNA transcription catalyzed by RNA polymerase (RNAP) has long been an important issue in biology. Experiments have revealed that RNAP can incorporate matched nucleotides selectively and proofread the incorporated mismatched nucleotides. However, systematic theoretical researches on RNAP fidelity are still lacking. In the last decade, several theories on RNA transcription have been proposed, but they only handled highly simplified models without considering the high-order neighbor effects and the oligonucleotides cleavage both of which are critical for the overall fidelity. In this paper, we regard RNA transcription as a binary copolymerization process and calculate the transcription fidelity by the steady-state copolymerization theory recently proposed by us for DNA replication. With this theory, the more realistic models considering higher-order neighbor effects, oligonucleotides cleavage, multi-step incorporation and multi-step cleavage can be rigorously handled.

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