芬斯勒流形上的Bochner不等式及热方程整体解的构造  

Bochner Inequality and the Constructions of the Global Solution of the Heat Equation on Finsler Manifolds

作　　者：程新跃 卿春燕 谭聪 CHENG Xinyue;QING Chunyan;TAN Cong(School of Mathematical Sciences,Chongqing Normal University,Chongqing 401331,China)

机构地区：[1]重庆师范大学数学科学学院,重庆401331

出　　处：《重庆师范大学学报（自然科学版）》2022年第2期69-75,共7页Journal of Chongqing Normal University:Natural Science

基　　金：国家自然科学基金项目(No.11871126);重庆师范大学研究基金(No.17XLB022)。

摘　　要：【目的】研究芬斯勒几何中的Bochner公式及与Laplacian算子相关的问题。【方法】利用偏微分方程及Sobolev空间的相关理论展开讨论。【结果】利用L;-梯度估计证明了一个重要的Bochner不等式,讨论了芬斯勒流形上热方程整体解的应用并构造了热方程的若干整体解。【结论】给出了一类Bochner公式成立的充分条件并构造了热方程的若干整体解。[Purposes]It mainly studies the Bochner formula and the problems related to Laplacian operators in Finsler geometry. [Methods] The discussions are carried out by using the theories of partial differential equations and Sobolev space. [Findings] An important Bochner inequality is proved by using of L;-gradient estimation, the applications of the global solution of the heat equation on the Finsler manifold are discussed and several global solutions of the heat equation are constructed.[Conclusions] A sufficient condition for a kind of Bochner formulas to hold is given and some global solutions of the heat equation are constructed.

关 键 词：芬斯勒流形 加权Ricci曲率 Bochner不等式 热方程 

分 类 号：O186.1[理学—数学]