Title:
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Some generalized comparison results in Finsler geometry and their applications (English) |
Author:
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Zhu, Yecheng |
Author:
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Hu, Wenming |
Language:
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English |
Journal:
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Archivum Mathematicum |
ISSN:
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0044-8753 (print) |
ISSN:
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1212-5059 (online) |
Volume:
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49 |
Issue:
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1 |
Year:
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2013 |
Pages:
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65-78 |
Summary lang:
|
English |
. |
Category:
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math |
. |
Summary:
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In this paper, we generalize the Hessian comparison theorems and Laplacian comparison theorems described in [16, 18], then give some applications under various curvature conditions. (English) |
Keyword:
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comparison theorem |
Keyword:
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Finsler geometry |
Keyword:
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distance function |
Keyword:
|
first eigenvalue |
MSC:
|
53B40 |
MSC:
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53C60 |
idZBL:
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Zbl 06321149 |
idMR:
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MR3073017 |
DOI:
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10.5817/AM2013-1-65 |
. |
Date available:
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2013-05-28T13:32:56Z |
Last updated:
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2014-07-30 |
Stable URL:
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http://hdl.handle.net/10338.dmlcz/143301 |
. |
Reference:
|
[1] Astola, L., Jalba, A., Balmashnova, E., Florack, L.: Finsler streamline tracking with single tensor orientation distribution function for high angular resolution diffusion imaging.J. Math. Imaging Vision 41 (2011), 170–181. Zbl 1255.68185, MR 2843892, 10.1007/s10851-011-0264-4 |
Reference:
|
[2] Bao, D., Chern, S. S., Shen, Z.: An Introduction to Riemann–Finsler Geometry.Springer, New York, 2000. Zbl 0954.53001, MR 1747675 |
Reference:
|
[3] Beil, R. G.: Finsler geometry and relativistic field theory.Found. Phys. 33 (2003), 1107–1127. MR 2012259, 10.1023/A:1025689902340 |
Reference:
|
[4] Busemann, H.: Intrinsic Area.Ann. Math. 48 (1947), 234–267. MR 0020626 |
Reference:
|
[5] Chen, Q., Xin, Y. L.: A generalized maximum principle and its applications in geometry.Amer. J. Math. 114 (1992), 335–366. Zbl 0776.53032, MR 1156569, 10.2307/2374707 |
Reference:
|
[6] Chen, X. Y., Shen, Z. M.: A comparison theorem on the Ricci curvature in projective geometry.Ann. Glob. Anal. Geom. 23 (2003), 14–155. Zbl 1043.53059, MR 1961373 |
Reference:
|
[7] Chern, S. S.: Local equivalence and Euclidean connections in Finsler space.Sci. Rep. Nat. Tsing Hua Univ. Ser. A 5 (1948), 95–121. MR 0031812 |
Reference:
|
[8] Kasue, A.: On a lower bound for the first eigenvalue of the Laplace operator on a Riemannian manifold.Ann. Sci. Ecole. Norm. Sup. 17 (1984), 31–44. Zbl 0553.53026, MR 0744066 |
Reference:
|
[9] Kim, C. W., Min, K.: Finsler metrics with positive constant flag curvature.Ann. Glob. Anal. Geom. 92 (2009), 70–79. Zbl 1170.53055, MR 2471989 |
Reference:
|
[10] Ohta, S.: Finsler interpolation inequalities.Calc. Var. Partial Differential Equations 36 (2009), 211–249. Zbl 1175.49044, MR 2546027, 10.1007/s00526-009-0227-4 |
Reference:
|
[11] Ohta, S.: Uniform convexity and smoothness, and their applications in Finsler geometry.Math. Ann. 343 (2009), 669–699. Zbl 1160.53033, MR 2480707, 10.1007/s00208-008-0286-4 |
Reference:
|
[12] Renesse, M.: Heat kernel comparison on Alexandrov spaces with curvature bounded below.Potential Anal. 21 (2004), 151–176. Zbl 1058.60063, MR 2058031, 10.1023/B:POTA.0000025376.45065.80 |
Reference:
|
[13] Shen, Z.: Volume comparision and its application in Riemann–Finsler geometry.Adv. Math. 128 (1997), 306–328. MR 1454401, 10.1006/aima.1997.1630 |
Reference:
|
[14] Shen, Z.: The Non-linear Laplacian Finsler Manifolds.The Theory of Finslerian Laplacians and Applications (Antonelli, P. L., Lackey, B. C., eds.), Kluwer Acad. Publ., Dordrecht, 1998, pp. 187–198. MR 1677366 |
Reference:
|
[15] Shen, Z.: Lectures on Finsler Geometry.World Scientific, Singapare, 2001. Zbl 0974.53002, MR 1845637 |
Reference:
|
[16] Shen, Z.: Curvature, distance and volume in Finsler geometry.IHES 311 (2003), 549–576. |
Reference:
|
[17] Wu, B. Y.: Some rigidity theorems for locally symmetrical Finsler manifolds.J. Geom. Phys. 58 (2008), 923–930. Zbl 1142.53328, MR 2426249, 10.1016/j.geomphys.2008.02.009 |
Reference:
|
[18] Wu, B. Y., Xin, Y. L.: Comparision theorem in Finsler geometry and their applications.Math. Ann. 337 (2007), 177–196. |
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