پیوندهای مفید
آمار
| تعداد نشریات | 8 |
| تعداد شماره‌ها | 414 |
| تعداد مقالات | 5,478 |
| تعداد مشاهده مقاله | 6,010,339 |
| تعداد دریافت فایل اصل مقاله | 5,299,919 |
Some fundamental problems in global Finsler geometry | ||
| AUT Journal of Mathematics and Computing | ||
| دوره 2، شماره 2، آذر 2021، صفحه 185-198 اصل مقاله (373.2 K) | ||
| نوع مقاله: Original Article | ||
| شناسه دیجیتال (DOI): 10.22060/ajmc.2021.20219.1060 | ||
| نویسنده | ||
| Xinyue Cheng* | ||
| School of Mathematical Sciences Chongqing Normal University Chongqing, China | ||
| چکیده | ||
| The geometry and analysis on Finsler manifolds is a very important part of Finsler geometry. In this survey article, we introduce some important and fundamental topics in global Finsler geometry and discuss the related properties and the relationships in them. In particular, we optimize and improve the various definitions of Lie derivatives on Finsler manifolds. Further, we also obtain an estimate of lower bound for the non-zero eigenvalues of the Finsler Laplacian under the condition that $\mathrm{Ric}_{N}\geq K >0 $. | ||
| کلیدواژه‌ها | ||
| Dual Finsler metric؛ Gradient vector field؛ Finsler Laplacian؛ Eigenvalue؛ Hessian؛ Lie derivative؛ Weighted Ricci curvature | ||
| مراجع | ||
|
[1] P. Antonelli and B. Lackey, The theory of Finslerian Laplacians and applications, MAIA 459, Dordrecht: Kluwer Academic Publishers, 1998.
[2] I. Bucataru and R. Miron, Finsler-Lagrange Geometry. Applications to Dynamical Systems, Romanian Academy Publication House, 2007.
[3] S. S. Chern and Z. Shen, Riemann-Finsler Geometry, Nankai Tracts in Mathematics, Vol. 6, World Scientific, 2005.
[4] Y. Ge and Z. Shen, Eigenvalues and eigenfunctions of metric measure manifolds, Proc. London. Math. Soc., 82(3) (2001), 725-746.
[5] Q. He, S. Yin and W. Zhao, Finsler harmonic maps and Laplace operators (Chinese), Science Press, Beijing, 2014.
[6] H. Hrimiuc and H. Shimada, On the L-duality between Finsler and Hamilton manifolds, Nonlinear World, 3 (1996), 613-641.
[7] J. L. Jauregui and W. Wylie, Conformal diffeomorphisms of gradient Ricci solitons and generalized quasi[1]Einstein manifolds, The Journal of Geometric Analysis, 25(1) (2015), 668-708.
[8] P. Joharinad and B. Bidabad, Conformal vector fields on Finsler spaces, Differential Geometry and its Appli[1]cations, 31(2013), 33-40.
[9] R. L. Lovas, Affine and projective vector fields on spray manifolds, Periodica Mathematica Hungarica, 48(1-2) (2004), 165-179.
[10] S. Ohta, Finsler interpolation inequalities, Calc. Var. Partial Differential Equations, 36 (2009), 211-249.
[11] S. Ohta and K. T. Sturm, Bochner-Weitzenbock formula and Li-Yau estimates on Finsler manifolds, Adv. Math., 252(2014), 429-448.
[12] P. Petersen, Riemannian Geometry (Third Edition), Graduate Texts in Mathematics, 171, Springer, 2016.
[13] Z. Shen, Lectures on Finsler Geometry, World Scientific, Singapore, 2001.
[14] Y.-B. Shen and Z. Shen, Introduction to Modern Finsler Geometry, Higher Education Press, Beijing, 2016.
[15] B. Thomas, A natural Finsler-Laplace operator, Israel J. Math., 196(1) (2013), 375-412.
[16] G. Wang and C. Xia, A sharp lower bound for the first eigenvalue on Finsler manifolds, Ann. Inst. H. Poincar´e Anal. Non Lin´eaire, 30(6) (2013), 983-996.
[17] Q. Xia, A sharp lower bound for the first eigenvalue on Finsler manifolds with nonnegative weighted Ricci curvature, Nonlinear Analysis, 117 (2015), 189-199.
[18] Q. Xia, Sharp spectral gap for the Finsler p-Laplacian, Sci China Math, 62 (2019), https://doi.org/10.1007/s11425-018-9510-5 .
[19] Q. Xia, Geometric and functional inequalities on Finsler manifolds, The Journal of Geometric Analysis, https://doi.org/10.1007/s12220-019-00192-5.
[20] 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: 1,222 تعداد دریافت فایل اصل مقاله: 746 |
||