Eigenvalue estimate for the Laplace operator on Finsler manifold with weighted Ricci curvature

Hajiaghasi, Sakineh; Azami, Shahroud

doi:10.22098/jfga.2025.15867.1137

دانشگاه محقق اردبیلی

تعداد نشریات	31
تعداد شماره‌ها	471
تعداد مقالات	4,150
تعداد مشاهده مقاله	6,931,137
تعداد دریافت فایل اصل مقاله	4,677,736

	Eigenvalue estimate for the Laplace operator on Finsler manifold with weighted Ricci curvature
Journal of Finsler Geometry and its Applications
دوره 6، شماره 1، 2025، صفحه 36-47 اصل مقاله (317.3 K)
نوع مقاله: Original Article
شناسه دیجیتال (DOI): 10.22098/jfga.2025.15867.1137
نویسندگان
Sakineh Hajiaghasi^* ¹؛ Shahroud Azami²
¹Department of pure Mathematics, Faculty of Science, Imam Khomeini International University, Qazvin, Iran.
²Department of pure mathematics, Faculty of sciences, Imam Khomeini International University, Qazvin, Iran.
چکیده
In this paper, we study about the rst eigenvalue of the bi-Laplace operator on Finsler manifolds. Considering a bounded weighted Ricci curvature on a complete Finsler manifold, we obtain an upper bound for the first eigenvalues of Buckling and Clamped plate problems related with the first eigenvalue of the laplace operator.
کلیدواژه‌ها
Eigenvalue problem؛ Finsler manifold؛ Weighted Ricci curvature

مراجع
1. M.S. Ashbaugh, On universal inequalities for the low eigenvalues of the buckling problem, Partial Differential Equations and Inverse Problem, Amer. Math. Soc. (2004), 13-31. 2. D. Bao, S.S. Chern and Z. Shen, An introduction to Riemann-Finsler Geometry, Springer-Verlag, New York, 2000. 3. M. Belloni, B. Kawohl and P. Juutinen, The p-Laplace eigenvalue problem as p -> 1 in a Finsler metric, J. Europ. Math. Soc. 8(2006), 123-138. 4. Q.M. Cheng and H.C. Yang, Universal bounds for eigenvalues of a buckling problem,Commun. Math. Phys. 262(2006), 663-675. 5. L. Friedlander, Some inequalities between Dirichlet and Neumann eigenvalues, Arch.Ration. Mech. Anal. 166 (1991), 153-160. 6. G.N. Hile, R.Z. Yeh, Inequality for eigenvalues of the biharmonic operator, Pac. J. Math.112(1984), 115-133. Eigenvalue estimate on Finsler laplacian 47 7. G. Huang and B. Ma, Some comparisons of Dirichlet, Newmann and Buckling Eigenvalues on Riemannian manifolds, Front. Math. 18(5) (2023), 1025-1035. 8. S. Ilias and A. Shouman, Inequalities between Dirichlet, Neumann and buckling eigenvalues on Riemannian manifolds, Calc. Var. Partial Differential Equations. 127(15) (2020). 9. H.A. Levine and H.F. Weinberger, Inequalities between Dirichlet and Neumann eigenvalues, Arch. Ration. Mech. Anal. 94(1986), 193-208. 10. S. Ohta, Finsler interpolation inequalities, Calc. Var. Partial differential equations 36 (2009), 211-249. 11. S. Ohta and K.T. Sturm, Bochner-Weitzenb¨ock formula and Li-Yau estimates on Finsler manifolds, Adv. Math. 252(2014), 429-448. 12. Sh. Pan and L. Zhang, The lower ans upper bounds of the first eigenvalues for the bi-Laplace operator on Finsler manifolds, Differ. Geom. Appl. 47(2016), 190-201. 13. Z. Shen, The non-linear Laplacian for Finsler manifolds. The theory of Finslerian Laplacians and applications, Proc. Conf. On Finsler Laplacians, Kluwer Acad. Press, Netherlands (1998). 14. S.T. Yin and Q. He, The first eigenvalue of Finsler p-Laplacian, Diff. Geom. Appl. 35(2014), 30-49. 15. S.T. Yin and Q. He, The first eigenfunctions and eigenvalue of the p-Laplacian on Finsler manifolds, Sci China Math. 59(2016), 1769-1794. 16. B. Y. Wu and Y. L. Xin, Comparison theorems in Finsler geometry and their applications, Math. Ann. 337 (2007), 177-196.
آمار تعداد مشاهده مقاله: 307 تعداد دریافت فایل اصل مقاله: 284

سامانه مدیریت نشریات علمی. قدرت گرفته از سیناوب

پیوندهای مفید

آمار

Eigenvalue estimate for the Laplace operator on Finsler manifold with weighted Ricci curvature