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Cheng, Xinyue, Wu, Pengsheng. (1401). Gradient estimates for positive global solutions of heat equation under closed Finsler-Ricci flow. سامانه مدیریت نشریات علمی, 3(1), 1-15. doi: 10.22098/jfga.2022.10956.1067
Xinyue Cheng; Pengsheng Wu. "Gradient estimates for positive global solutions of heat equation under closed Finsler-Ricci flow". سامانه مدیریت نشریات علمی, 3, 1, 1401, 1-15. doi: 10.22098/jfga.2022.10956.1067
Cheng, Xinyue, Wu, Pengsheng. (1401). 'Gradient estimates for positive global solutions of heat equation under closed Finsler-Ricci flow', سامانه مدیریت نشریات علمی, 3(1), pp. 1-15. doi: 10.22098/jfga.2022.10956.1067
Cheng, Xinyue, Wu, Pengsheng. Gradient estimates for positive global solutions of heat equation under closed Finsler-Ricci flow. سامانه مدیریت نشریات علمی, 1401; 3(1): 1-15. doi: 10.22098/jfga.2022.10956.1067

Gradient estimates for positive global solutions of heat equation under closed Finsler-Ricci flow

Journal of Finsler Geometry and its Applications
مقاله 1، دوره 3، شماره 1، مهر 2022، صفحه 1-15    اصل مقاله (119.03 K)
نوع مقاله: Original Article
شناسه دیجیتال (DOI): 10.22098/jfga.2022.10956.1067
نویسندگان
Xinyue Cheng* 1؛ Pengsheng Wu2
1School of Mathematical Sciences, Chongqing Normal University, Chongqing, China
2School of Mathematical Sciences, Chongqing Normal University, Chongqing, China
چکیده
In this paper, we establish first order gradient estimates for positive global solutions of the heat equation under closed Finsler-Ricci flow with weighted Ricci curvature RicN bounded below, where N∈ (n,∞). As an application, we derive the corresponding Harnack inequality. Our results are the generalizations and the supplements of the previous known related results.
کلیدواژه‌ها
Finsler-Ricci flow؛ gradient estimate؛ heat equation؛ weighted Ricci curvature؛ Ricci curvature tensor
مراجع
  • 1. D. Bao, S.-S. Chern and Z. Shen, An Introduction to Riemann-Finsler Geometry, GTM
    200, Springer, New York, 2000.
  • 2. M. Bailesteanu, X. Cao and A. Pulemotov, Gradient estimates for the heat equation
    under the Ricci flow, Journal of Functional Analysis, 258(2010), 3517-3542.
  • 3. S.-S. Chern and Z. Shen, Riemann-Finsler Geometry, Nankai Tracts in Mathematics,
    Vol. 6, World Scientific, 2005.
  • 4. X. Cheng, Some fundamental problems in global Finsler geometry, AUT Journal of Mathematics and Computing, 2(2)(2021), 185-198.
  • 5. X. Cheng, Gradient estimates for positive solutions of heat equations under FinslerRicci flow, Journal of Mathematical Analysis and Applications, 508(2)(2022), article
    nonumber: 125897.
  • 6. L. C. Evans, Partial Differential Equations, American Mathematical Society, Providence,
    RI, 1998.
  • 7. R. S. Hamilton, The formation of singularities in the Ricci flow, Surv. Differ. Geom.,
    vol. II, International Press, Cambridge, MA, 1995, 7-136.
  • 8. P. Li and S. T. Yau, On the parabolic kernel of the Schr¨odinger operator, Acta Mathematica, 156(1)(1986), 153-201.
  • 9. S. Lakzian, Differential Harnack estimates for positive solutions to heat equation under
    Finsler-Ricci flow, Pacific J. Math., 278(2)(2015), 447-462.
  • 10. S. Liu, Gradient estimates for solutions of the heat equation under Ricci flow, Pacific J.
    Math., 243(1)(2009), 165-180.
  • 11. S. Ohta and K.-T. Sturm, Heat flow on Finsler manifolds, Comm. Pure Appl. Math.,
    62(10)(2009), 1386-1433.
  • 12. S. Ohta and K.-T. Sturm, Bochner-Weitzenbo¨ck formula and Li-Yau estimates on
    Finsler manifolds, Advances in Mathematics, 252(2014), 429-448.
  • 13. Z. Shen, Lectures on Finsler Geometry, World Scientific, Singapore, 2001.
  • 14. B. Wu and Y. Xin, Comparison theorems in Finsler geometry and their applications,
    Math. Ann., 337(2007), 177-196.
  • 15. Q. Xia, Li-Yau’s estimates for the heat flow on complete Finsler manifolds, preprint,
    2020.
  • 16. F. Zeng and Q. He, Gradient estimates for a nonlinear heat equation under the FinslerRicci flow, Mathematica Slovaca, 69(2019), 409-424. 
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