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EIGENVALUE MONOTONICITY OF (p, q)-LAPLACIAN ALONG THE RICCI-BOURGUIGNON FLOW
Azami, Shahroud Korean Mathematical Society 2019 대한수학회논문집 Vol.34 No.1
In this paper we study monotonicity the first eigenvalue for a class of (p, q)-Laplace operator acting on the space of functions on a closed Riemannian manifold. We find the first variation formula for the first eigenvalue of a class of (p, q)-Laplacians on a closed Riemannian manifold evolving by the Ricci-Bourguignon flow and show that the first eigenvalue on a closed Riemannian manifold along the Ricci-Bourguignon flow is increasing provided some conditions. At the end of paper, we find some applications in 2-dimensional and 3-dimensional manifolds.
RICCI 𝜌-SOLITONS ON 3-DIMENSIONAL 𝜂-EINSTEIN ALMOST KENMOTSU MANIFOLDS
Azami, Shahroud,Fasihi-Ramandi, Ghodratallah Korean Mathematical Society 2020 대한수학회논문집 Vol.35 No.2
The notion of quasi-Einstein metric in theoretical physics and in relation with string theory is equivalent to the notion of Ricci soliton in differential geometry. Quasi-Einstein metrics or Ricci solitons serve also as solution to Ricci flow equation, which is an evolution equation for Riemannian metrics on a Riemannian manifold. Quasi-Einstein metrics are subject of great interest in both mathematics and theoretical physics. In this paper the notion of Ricci 𝜌-soliton as a generalization of Ricci soliton is defined. We are motivated by the Ricci-Bourguignon flow to define this concept. We show that if a 3-dimensional almost Kenmotsu Einstein manifold M is a 𝜌-soliton, then M is a Kenmotsu manifold of constant sectional curvature -1 and the 𝜌-soliton is expanding with λ = 2.
Azami, Shahroud Korean Mathematical Society 2020 대한수학회논문집 Vol.35 No.3
In this article we study the evolution and monotonicity of the first non-zero eigenvalue of weighted p-Laplacian operator which it acting on the space of functions on closed oriented Riemannian n-manifolds along the extended Ricci flow and normalized extended Ricci flow. We show that the first eigenvalue of weighted p-Laplacian operator diverges as t approaches to maximal existence time. Also, we obtain evolution formulas of the first eigenvalue of weighted p-Laplacian operator along the normalized extended Ricci flow and using it we find some monotone quantities along the normalized extended Ricci flow under the certain geometric conditions.
Evolution of the First Eigenvalue of Weighted p-Laplacian along the Yamabe Flow
Azami, Shahroud Department of Mathematics 2019 Kyungpook mathematical journal Vol.59 No.2
Let M be an n-dimensional closed Riemannian manifold with metric g, $d{\mu}=e^{-{\phi}(x)}d{\nu}$ be the weighted measure and ${\Delta}_{p,{\phi}}$ be the weighted p-Laplacian. In this article we will study the evolution and monotonicity for the first nonzero eigenvalue problem of the weighted p-Laplace operator acting on the space of functions along the Yamabe flow on closed Riemannian manifolds. We find the first variation formula of it along the Yamabe flow. We obtain various monotonic quantities and give an example.
THE SET OF ZOLL METRICS IS NOT PRESERVED BY SOME GEOMETRIC FLOWS
Azami, Shahroud,Fasihi-Ramandi, Ghodratallah Korean Mathematical Society 2019 대한수학회논문집 Vol.34 No.3
The geodesics on the round 2-sphere $S^2$ are all simple closed curves of equal length. In 1903 Otto Zoll introduced other Riemannian surfaces with the same property. After that, his name is attached to the Riemannian manifolds whose geodesics are all simple closed curves of the same length. The question that "whether or not the set of Zoll metrics on 2-sphere $S^2$ is connected?" is still an outstanding open problem in the theory of Zoll manifolds. In the present paper, continuing the work of D. Jane for the case of the Ricci flow, we show that a naive application of some famous geometric flows does not work to answer this problem. In fact, we identify an attribute of Zoll manifolds and prove that along the geometric flows this quantity no longer reflects a Zoll metric. At the end, we will establish an alternative proof of this fact.
THE FIRST EIGENVALUE OF SOME (p, q)-LAPLACIAN AND GEOMETRIC ESTIMATES
Azami, Shahroud Korean Mathematical Society 2018 대한수학회논문집 Vol.33 No.1
We study the nonlinear eigenvalue problem for some of the (p, q)-Laplacian on compact manifolds with zero boundary condition. In particular, we obtain some geometric estimates for the first eigenvalue.
Breast Cancer Screening Barriers from the Womans Perspective: a Meta-synthesis
Azami-Aghdash, Saber,Ghojazadeh, Morteza,Sheyklo, Sepideh Gareh,Daemi, Amin,Kolahdouzan, Kasra,Mohseni, Mohammad,Moosavi, Ahmad Asian Pacific Journal of Cancer Prevention 2015 Asian Pacific journal of cancer prevention Vol.16 No.8
Background: The principal aim of health service providers in the field of breast cancer is to detect and treat lesions at an appropriate time. Therefore, identification of barriers to screening can be very helpful. The present study aimed to systematically review the qualitative studies for extracting and reporting the barriers of screening for breast cancer from the womans perspective. Materials and Methods: In this systematic review; Pubmed, Google Scholar, Ovid Scopus, Cochrane Library, Iranmedex, and SID were searched using the keywords: screening barriers, cancer, qualitative studies, breast and their Persian equivalents, and the needed data were extracted and analyzed using an extraction table. To assess the quality of the studies, the Critical Appraisal Skills Programme (CASP) tool was used. Results: From 2,134 related articles that were found, 21 articles were eventually included in the study. The most important barriers from the point of view of 1,084 women were lack of knowledge, access barriers (financial, geographical, cultural), fear (of results and pain), performance of service providers, women's beliefs, procrastination of screening, embarrassment, long wait for getting an appointment, language problems, and previous negative experiences. Articles' assessment score was 68.9. Conclusions: Increasing women's knowledge, reducing the costs of screening services, cultural promotion for screening, presenting less painful methods, changing beliefs of health service providers, provision of privacy for giving service, decreasing the waiting time, and providing high quality services in a respectful manner can be effective ways to increase breast cancer screening.
Shahroud Azami 호남수학회 2023 호남수학학술지 Vol.45 No.4
In this paper, we study quasi-Sasakian 3-dimensional manifolds admitting generalized η-Ricci solitons associated to the Schoutenvan Kampen connection. We give an example of generalized η-Ricci solitons on a quasi-Sasakian 3-dimensional manifold with respect to the Schouten-van Kampen connection to prove our results.
New volume comparison with almost Ricci soliton
Shahroud Azami,Sakineh Hajiaghasi 대한수학회 2022 대한수학회논문집 Vol.37 No.3
In this paper we consider a condition on the Ricci curvature involving vector fields which enabled us to achieve new results for volume comparison and Laplacian comparison. These results in special case obtained with considering volume non-collapsing condition. Also, by applying this condition we get new results of volume comparison for almost Ricci solitons.
Generalized hyperbolic geometric flow
Shahroud Azami,Ghodratallah Fasihi-Ramandi,Vahid Pirhadi 대한수학회 2023 대한수학회논문집 Vol.38 No.2
In the present paper, we consider a kind of generalized hyperbolic geometric flow which has a gradient form. Firstly, we establish the existence and uniqueness for the solution of this flow on an $n$-dimensional closed Riemannian manifold. Then, we give the evolution of some geometric structures of the manifold along this flow.