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Cheng, Xinyue, Cheng, Hong, Zhang, Xibin. (1401). Some volume comparison theorems on Finsler manifolds of weighted Ricci curvature bounded below. سامانه مدیریت نشریات علمی, 3(2), 1-12. doi: 10.22098/jfga.2022.11723.1072
Xinyue Cheng; Hong Cheng; Xibin Zhang. "Some volume comparison theorems on Finsler manifolds of weighted Ricci curvature bounded below". سامانه مدیریت نشریات علمی, 3, 2, 1401, 1-12. doi: 10.22098/jfga.2022.11723.1072
Cheng, Xinyue, Cheng, Hong, Zhang, Xibin. (1401). 'Some volume comparison theorems on Finsler manifolds of weighted Ricci curvature bounded below', سامانه مدیریت نشریات علمی, 3(2), pp. 1-12. doi: 10.22098/jfga.2022.11723.1072
Cheng, Xinyue, Cheng, Hong, Zhang, Xibin. Some volume comparison theorems on Finsler manifolds of weighted Ricci curvature bounded below. سامانه مدیریت نشریات علمی, 1401; 3(2): 1-12. doi: 10.22098/jfga.2022.11723.1072

Some volume comparison theorems on Finsler manifolds of weighted Ricci curvature bounded below

Journal of Finsler Geometry and its Applications
دوره 3، شماره 2، اسفند 2022، صفحه 1-12    اصل مقاله (106.24 K)
نوع مقاله: Original Article
شناسه دیجیتال (DOI): 10.22098/jfga.2022.11723.1072
نویسندگان
Xinyue Cheng* ؛ Hong Cheng؛ Xibin Zhang
School of Mathematical Sciences, Chongqing Normal University, Chongqing, China
چکیده
This paper mainly studies the volume comparison in Finsler geometry under the condition that the weighted Ricci curvature Ric∞ has a lower bound. By using the Laplacian comparison theorems of distance function, we characterize the growth ratio of the volume coefficients. Further, some volume comparison theorems of Bishop-Gromov type are obtained.
کلیدواژه‌ها
: volume comparison؛ the weighted Ricci curvature؛ Laplacian comparison theorem؛ distance function؛ volume coefficient
مراجع
  • 1. D. Bao, S.-S. Chern and Z. Shen, An Introduction to Riemann-Finsler Geometry, GTM
    200, Springer, New York, 2000.
  • 2. X. Cheng and Z. Shen, Some inequalities on Finsler manifolds with weighted Ricci curvature bounded below, Results in Mathematics, 77(2022), Article number: 70 (23 pages).
  • 3. S.-S. Chern and Z. Shen, Riemann-Finsler Geometry, Nankai Tracts in Mathematics,
    Vol. 6, World Scientific, 2005.
  • 4. R. M. Howard, Arbitrarily accurate analytical approximations for the error function,
    Mathematical and Computational Applications, 27(1)(2022), Article number: 14 (47
    pages).
  • 5. S. Ohta, Finsler interpolation inequalities, Calculus of Variations and Partial Differential
    Equations, 36(2009), 211-249.
  • 6. Z. Shen, Volume comparison and its applications in Riemann-Finsler geometry, Advances in Mathematics, 128(2)(1997), 306-328.
  • 7. Z. Shen, Lectures on Finsler Geometry, World Scientific, Singapore, 2001.
  • 8. Z. Shen, Weighted Ricci curvature in Riemann-Finsler geometry, AUT J. Math. Com.,
    2(2)(2021), 117-136.
  • 9. G. Wei and W. Wylie, Comparison geometry for the Bakry-Emery Ricci tensor, J. Diff.
    Geom., 83(2009), 377-405.
  • 10. B. Wu and Y. Xin, Comparison theorems in Finsler geometry and their applications,
    Math. Ann., 337(2007), 177-196.
  • 11. Q. Xia, Geometric and functional inequalities on Finsler manifolds, The Journal of
    Geometric Analysis, 30(3)(2020), 3099-3148.
  • 12. S. Yin, Comparison theorems on Finsler manifolds with weighted Ricci curvature bounded
    below, Front. Math. China, 13(2018), 435-448.
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