Article
Full entry |
PDF
(0.4 MB)
Feedback
PDF
(0.4 MB)
Feedback
Keywords:
comparison theorem; Finsler geometry; distance function; first eigenvalue
comparison theorem; Finsler geometry; distance function; first eigenvalue
Summary:
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.
References:
[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. DOI 10.1007/s10851-011-0264-4 | MR 2843892 | Zbl 1255.68185
[2] Bao, D., Chern, S. S., Shen, Z.: An Introduction to Riemann–Finsler Geometry. Springer, New York, 2000. MR 1747675 | Zbl 0954.53001
[3] Beil, R. G.: Finsler geometry and relativistic field theory. Found. Phys. 33 (2003), 1107–1127. DOI 10.1023/A:1025689902340 | MR 2012259
[4] Busemann, H.: Intrinsic Area. Ann. Math. 48 (1947), 234–267. MR 0020626
[5] Chen, Q., Xin, Y. L.: A generalized maximum principle and its applications in geometry. Amer. J. Math. 114 (1992), 335–366. DOI 10.2307/2374707 | MR 1156569 | Zbl 0776.53032
[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. MR 1961373 | Zbl 1043.53059
[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
[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. MR 0744066 | Zbl 0553.53026
[9] Kim, C. W., Min, K.: Finsler metrics with positive constant flag curvature. Ann. Glob. Anal. Geom. 92 (2009), 70–79. MR 2471989 | Zbl 1170.53055
[10] Ohta, S.: Finsler interpolation inequalities. Calc. Var. Partial Differential Equations 36 (2009), 211–249. DOI 10.1007/s00526-009-0227-4 | MR 2546027 | Zbl 1175.49044
[11] Ohta, S.: Uniform convexity and smoothness, and their applications in Finsler geometry. Math. Ann. 343 (2009), 669–699. DOI 10.1007/s00208-008-0286-4 | MR 2480707 | Zbl 1160.53033
[12] Renesse, M.: Heat kernel comparison on Alexandrov spaces with curvature bounded below. Potential Anal. 21 (2004), 151–176. DOI 10.1023/B:POTA.0000025376.45065.80 | MR 2058031 | Zbl 1058.60063
[13] Shen, Z.: Volume comparision and its application in Riemann–Finsler geometry. Adv. Math. 128 (1997), 306–328. DOI 10.1006/aima.1997.1630 | MR 1454401
[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
[15] Shen, Z.: Lectures on Finsler Geometry. World Scientific, Singapare, 2001. MR 1845637 | Zbl 0974.53002
[16] Shen, Z.: Curvature, distance and volume in Finsler geometry. IHES 311 (2003), 549–576.
[17] Wu, B. Y.: Some rigidity theorems for locally symmetrical Finsler manifolds. J. Geom. Phys. 58 (2008), 923–930. DOI 10.1016/j.geomphys.2008.02.009 | MR 2426249 | Zbl 1142.53328
[18] Wu, B. Y., Xin, Y. L.: Comparision theorem in Finsler geometry and their applications. Math. Ann. 337 (2007), 177–196.
Search
Partner of
