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Gradient estimate of equations with potential under the almost Ricci soliton condition | ||
| International Journal of Nonlinear Analysis and Applications | ||
| مقالات آماده انتشار، اصلاح شده برای چاپ، انتشار آنلاین از تاریخ 12 خرداد 1404 اصل مقاله (448.86 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2023.28958.4031 | ||
| 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 | ||
| تاریخ دریافت: 20 آبان 1401، تاریخ بازنگری: 20 مهر 1402، تاریخ پذیرش: 01 دی 1402 | ||
| چکیده | ||
| Using volume comparison theorems and the Sobolev inequality with almost Ricci solitons, we study an important version of the gradient estimate for the solutions of $\Delta u=f+Hu$, for some function $f$, $H$, and we obtain an upper bound for the gradient of $u$ on almost Ricci solitons. | ||
| کلیدواژهها | ||
| Sobolev constant؛ Gradient estimate؛ Ricci soliton؛ Bakry-{\'E}mery Ricci curvature | ||
| مراجع | ||
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[1] S. Azami and S. Hajiaghasi, New volume comparison with almost Ricci soliton, Commun. Korean Math. Soc. 37 (2022), no. 3, 839–849. [2] R.H. Bamler, Entropy and heat kernel bounds on a Ricci flow background, arXiv:2008.07093v3 [math.DG] (2021). [3] A. Barros and E. Ribeiro Jr, Some characterizations for compact almost Ricci solitons, Proc. Amer. Math. Soc. 140 (2012), no. 3, 1033–1040. [4] X. Cao and R.S. Hamilton, Differential Harnack estimates for time-dependent heat equations, Geom. Funct. Anal. 19 (2009), no. 4, 989–1000. [5] X. Dai, G. Wei, and Z. Zhang, Local Sobolev constant estimate for integral Ricci curvature bounds, Adv. Math. 325 (2018), 1–33. [6] S. Deshmukh, Almost Ricci solitons isometric to spheres, Int. J. Geometric Meth. Mod. Phys. 16 (2019), no. 5 1950073. [7] S. Deshmukh and H. Al-Sodais, A note on almost Ricci soliton, Anal. Math. Phys. 10 (2020), 1–11. [8] S. Deshmukh, H. Alsodais, and N. Bin Turki, Some results on Ricci almost solitons, Symmetry 13 (2021), 430. [9] Q. Han and F. Lin, Elliptic Partial Differential Equations, American Mathematical Society, 1997. [10] W. Hebisch and L. Saloff-Costa, On the relation between elliptic and parabolic Harnack inequalities Ann. Inst. Fourier 51 (2001), no. 5, 1437–1481. [11] A. Ghosh, Ricci almost solitons satisfying certain conditions on the potential vector field, Publ. Math. Debrecen 87 (2015), no. 1-2, 103–110. [12] P. Petersen and G.F. Wei, Analysis and geometry on manifolds with integral Ricci curvature bounds II, Trans. Amer. Math. Soc. 353 (2000), no. 2, 457–478. [13] S. Pigola, M. Rigoli, M. Rimoldi, and A.G. Setti, Ricci almost solitons, Ann. Scuola Normale Super. Pisa-Classe Sci. 10 (2011), no. 4, 757–799. [14] C. Rose, Heat kernel upper bound on Riemannian manifolds with locally uniform Ricci curvature integral bounds, J. Geom. Anal. 27 (2017), no. 2, 1737–1750. [15] R. Sharma, Almost Ricci solitons and K-contact geometry, Monatsh. Math. 175 (2014), 621–628. [16] L. Wang and G. Wei, Local Sobolev constant estimate for integral Bakry-Emery Ricci curvature, Pacific J. Math. 300 (2019), no. 1, 233–256. [17] G. Wei, R. Ye, A Neumann type maximum principle for the Laplace operator on compact Riemannian manifolds, Journal of Geometric Analysis 19 (2009), no. 3, 719-736. [18] Q.S. Zhang, Some gradient estimates for the heat equation on domains and for an equation by Perelman, Int. Math. Res. Not. 2006 (2006), Art.ID92314. [19] Q.S. Zhang and M. Zhu, New volume comparison results and applications to degeneration of Riemannian metrics, Adv. Math. 352 (2019), 1096–1154. | ||
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