广义调和映射和调和形式的相关问题

发布时间：2018-06-18 13:48

  本文选题：p-调和1-形式 + 局部共形平坦　； 参考：《信阳师范学院》2017年硕士论文

【摘要】：本文通过几何分析的方法研究了一些广义的调和映射及其性质,主要内容包括局部共形平坦黎曼流形上的Lp p-调和1-形式的一些消灭定理和有限性定理,还有CC-稳态映射的能量单调公式及刘维尔型结果,以及具有非负Bakry-Emery伪Hermitian Ricci曲率的完备非紧伪Hermitian流形上的非线性次抛物方程的次梯度估计.本文共分为四章.第一章简单介绍了所研究问题的发展历史,并叙述了我们得到的主要结果.第二章研究了局部共形平坦黎曼流形上的Lpp调和1-形式,当这个局部共形平坦黎曼流形在迹为零的Ricci张量上满足一个积分拼挤条件,并且其中数量曲率满足拼挤曲率条件或者M的Laplace-Beltrami算子的第一个特征值被一个适当的常数控制时,我们在这个局部共形平坦黎曼流形上得到一些关于Lp p-调和1-形式的消灭定理和有限性定理.第三章引进了从黎曼流形到伪Hermitian流形上的映射的水平泛函ΦH.该泛函的临界映射称为CC-稳态映射.利用水平应力能量张量,得到了该类映射的CC-稳态映射的能量单调公式及刘维尔型结果.第四章首先介绍了伪Hermitian(2n+1)-流形中的一些基本知识,其次主要考虑一个满足CR次Laplacian比较定理并且具有m-Bakry-Emery(或∞-Bakry-Emery)伪Hermitian Ricci曲率条件的完备非紧伪Hermitian(2n + 1)-流形,得到了该流形上的非线性次抛物方程的正解的次梯度估计.
[Abstract]:In this paper, we study some generalized harmonic mappings and their properties by means of geometric analysis. The main contents include some annihilation theorems and finiteness theorems of LP p-harmonic 1-form on locally conformal flat Riemannian manifolds. There are energy monotone formulas for CC-steady-state maps and Liouville type results, and subgradient estimates of nonlinear subparabolic equations on complete noncompact pseudo Hermitian manifolds with nonnegative Bakry-Emery pseudo Hermitian Ricci curvature. This paper is divided into four chapters. The first chapter briefly introduces the development history of the problems studied, and describes the main results we have obtained. In chapter 2, we study the LPP harmonic 1-form on a locally conformal flat Riemannian manifold, when the locally conformal flat Riemannian manifold satisfies an integral squeezing condition on the locally conformal flat Riemannian manifold with zero trace. And where the scalar curvature satisfies the squeezing curvature condition or the first eigenvalue of the Laplace-Beltrami operator of M is controlled by an appropriate constant, In this locally conformal flat Riemannian manifold, we obtain some annihilation theorems and finiteness theorems on LP pharmonic 1-form. In chapter 3, we introduce the horizontal functional 桅 H of mapping from Riemannian manifold to pseudo Hermitian manifold. The critical mapping of the functional is called CC-Steady-State Mapping. By using the horizontal stress energy Zhang Liang, the energy monotone formula and the Liouville type result of the CC-steady-state mapping of this kind of mapping are obtained. In chapter 4, we first introduce some basic knowledge of pseudo Hermitianian 2n 1- manifolds, then we consider a complete noncompact Hermitianian 2n 1- manifold with m-Bakry-Emery (or 鈭，

本文编号：2035693