|
|
- 2017
f-调和函数的Hess矩阵的估计及其在分裂定理中的应用
|
Abstract:
摘要： 得到了f-调和函数的Hess矩阵的一个新的估计。 运用这个新的估计,对具有加权Poincaré不等式以及Bakry-émery Ricci曲率的下界是负函数的光滑度量测度空间上的一个分裂定理进行了改进。
Abstract: A new estimate for the Hessian of f-harmonic functions is obtained. Using the new estimate, we improve a splitting theorem on smooth metric measure space with weighted Poincaré inequality under the condition that the Bakry-émery Ricci curvature is bounded from below by some negative functions
| [1] | CHEEGER J, GROMOLL D. The splitting theorem for manifolds of nonnegative Ricci curvature[J]. J Differential Geom, 1971, 6:119-128. |
| [2] | TOPONOGOV V A. Riemannian spaces containing straight lines[J]. Dokl Akad Nauk SSSR, 1959, 127:977-979. |
| [3] | WANG Linfeng. A splitting theorem for the weighted measure[J]. Ann Global Anal Geom, 2012, 42:79-89. |
| [4] | WU Jiayong. A note on the splitting theorem for the weighted measure[J]. Ann Glob Anal Geom, 2013, 43:287-298. |
| [5] | LICHNEROWICZ A. Varietes riemanniennes a tensor C non negatif[J]. C R Acad Sc Paris Serie A, 1970, 271:A650-A653. |
| [6] | MUNTEANU O, WANG J P. Analysis of weighted Laplacians and applications to Ricci solitons[J]. Comm Anal Geom, 2012, 20:55-94. |
| [7] | DUNG N T, SUNG C J A. Smooth metric measure spaces with weighted Poincaré inequality[J]. Math Z, 2013, 273:613-632. |
| [8] | DUNG N T, SUNG C J A. Manifolds with a weighted Poincaré inequality[J]. Proc Amer Math Soc, 2014, 142:1783-1794. |
| [9] | DUNG N T. A splitting theorem on smooth metric measure spaces[J]. Arch Math, 2012, 99:179-187. |
| [10] | PETER L, WANG Jiaping. Weighted Poincaré inequality and rigidly of complete manifolds[J]. Ann Scient, éc Norm Sup, 4E série, Tome, 2006, 39:921-982. |
| [11] | WEI Guofang, WYLIE W. Comparison geometry for the Bakry-émery Ricci tensor[J]. J Differential Geom, 2009, 83:377-405. |
| [12] | SU Yanhui, ZHANG Huichun. Rigidity of manifolds with Bakry-émery Ricci curvature bounded below[J]. Geom Dedicata, 2012, 160:321-331. |
| [13] | FANG Fuquan, LI Xiangdong, ZHANG Zhenlei. Two generalizations of Gheeger-Gromoll splitting theorem via Bakry-émery Ricci curvature[J]. Ann Inst Fourier, 2009, 59:563-573. |
