The first eigenvalue of Finsler p-Laplacian
The first eigenvalue of Finsler p-Laplacian
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DOI：
10.1016/j.difgeo.2014.04.009
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发表时间：
2014-08
影响因子：
0.5
通讯作者：
S. Yin;Qun He
中科院分区：
文献类型：
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作者：
S. Yin;Qun He
定义了Finsler流形上的p- laplacian的特征值和特征函数为其正则能量泛函的临界值和临界点。在此基础上，我们将黎曼流形上的p-拉普拉斯特征值比较定理，如Lichnerowicz型估计、Obata型定理和Mckean型定理推广到Finsler集合。不仅如此，我们得到的Lichnerowicz型估计甚至比黎曼几何中的相应估计更好。
The eigenvalues and eigenfunctions ofp-Laplacian on Finsler manifolds are defined to be critical values and critical points of its canonical energy functional. Based on it, we generalize some eigenvalue comparison theorems ofp-Laplacian on Riemannian manifolds, such as Lichnerowicz type estimate, Obata type theorem and Mckean type theorem, to the Finsler setting. Not only that, the Lichnerowicz type estimate we obtained is even better than the corresponding one in Riemannian geometry.