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Author:Abimbola Abolarinwa
Data Source:[J].Mediterranean Journal of Mathematics(IF 0.641), 2016, Vol.13 (5), pp.3185-3204Springer
Abstract:Abstract In this paper, we prove several Harnack estimates for positive solutions to the heat-type equations with respect to time-dependent Riemannian metric evolving by the geometric flow. In particular, we obtain Li–Yau type estimates and Perelman type differential Harnack...
Author:... Michael Ajala , Abimbola Abolarinwa , Olufunmilade Omisanjo
Data Source:[J].Nigerian Journal of Surgery, 2016, Vol.22 (1), pp.5-8Wolters Kluwer
Abstract:Introduction: Serum prostate specific antigen (PSA) levels increase with age and varies among different races and communities. The study was aimed at defining the age-specific reference ranges of serum PSA in our environment. Methods: We evaluated the relationship between ag...
Author:Abimbola Abolarinwa , Adekunle Adebayo ...
Data Source:[J].Nigerian Medical Journal, 2016, Vol.57 (4), pp.238-241Wolters Kluwer
Abstract:Background: Prostate cancer is the most commonly diagnosed cancer in men in Nigeria and most cases present when the disease is already in an advanced stage. Radical prostatectomy for early prostate cancer is therefore not a commonly performed operation by urologists in Nigeria. W...
Author:Abimbola Abolarinwa
Data Source:[J].International Journal of Analysis and Applications, 2014, Vol.6 (1)Etamaths Publishing
Abstract:In this paper we prove a new monotonicity formula for the heat equation via a generalized family of entropy functionals. This family of entropy formulas generalizes both Perelman’s entropy for evolving metric and Ni’s entropy on static manifold. We show that this entropy sat...
Author:Abimbola Abolarinwa
Data Source:[J].Afrika Matematika, 2016, Vol.27 (1-2), pp.169-186Springer
Abstract:Abstract This paper is concerned with Sobolev-type inequalities and upper bound for the fundamental solution to the heat-type equation defined on compact manifold whose metric evolves by the generalized geometric flow. It turns out that the pointwise estimates obtained in this pa...
Author:Abimbola Abolarinwa
Data Source:[J].International Journal of Analysis and Applications, 2014, Vol.6 (1), pp.1-17Etamaths Publishing
Abstract:In this paper we prove a new monotonicity formula for the heat equation via a generalized family of entropy functionals. This family of entropy formulas generalizes both Perelman’s entropy for evolving metric and Ni’s entropy on static manifold. We show that this entropy sat...
Author:Abimbola Abolarinwa
Data Source:[J].Pacific Journal of Mathematics(IF 0.465), 2015, Vol.278 (2), pp.257-290MSP
Abstract:This paper introduces a new family of entropy functionals which is provedto be monotonically nondecreasing along the Ricci-harmonic map heat flow.Some of the consequences of the monotonicity are combined to derivegradient estimates and Harnack inequalities for all positive soluti...
Author:Abimbola Abolarinwa
Data Source:[J].Asian-European Journal of Mathematics, 2015, Vol.08 (04)World Scientific Publishing
Abstract:We prove (local and global) differential Harnack inequalities for all positive solutions to the geometric conjugate heat equation coupled to the forward in time Ricci flow. In this case, the diffusion operator is perturbed with the curvature operator, precisely, the Laplace–...
Author:Abimbola Abolarinwa
Data Source:[J].Journal of Applied Analysis, 2015, Vol.21 (2), pp.147-160De Gruyter
Abstract:Abstract We study the evolution and monotonicity of the eigenvalues of p -Laplace operator on an m -dimensional compact Riemannianmanifold M whose metric g ( t ) evolves by the Ricci-harmonic flow. The firstnonzero eigenvalue is proved to be monotonically nondecreasing along...

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