本文選題：p-調(diào)和1-形式 + 局部共形平坦　； 參考：《信陽師范學院》2017年碩士論文

【摘要】：本文通過幾何分析的方法研究了一些廣義的調(diào)和映射及其性質(zhì),主要內(nèi)容包括局部共形平坦黎曼流形上的Lp p-調(diào)和1-形式的一些消滅定理和有限性定理,還有CC-穩(wěn)態(tài)映射的能量單調(diào)公式及劉維爾型結(jié)果,以及具有非負Bakry-Emery偽Hermitian Ricci曲率的完備非緊偽Hermitian流形上的非線性次拋物方程的次梯度估計.本文共分為四章.第一章簡單介紹了所研究問題的發(fā)展歷史,并敘述了我們得到的主要結(jié)果.第二章研究了局部共形平坦黎曼流形上的Lpp調(diào)和1-形式,當這個局部共形平坦黎曼流形在跡為零的Ricci張量上滿足一個積分拼擠條件,并且其中數(shù)量曲率滿足拼擠曲率條件或者M的Laplace-Beltrami算子的第一個特征值被一個適當?shù)某?shù)控制時,我們在這個局部共形平坦黎曼流形上得到一些關(guān)于Lp p-調(diào)和1-形式的消滅定理和有限性定理.第三章引進了從黎曼流形到偽Hermitian流形上的映射的水平泛函ΦH.該泛函的臨界映射稱為CC-穩(wěn)態(tài)映射.利用水平應力能量張量,得到了該類映射的CC-穩(wěn)態(tài)映射的能量單調(diào)公式及劉維爾型結(jié)果.第四章首先介紹了偽Hermitian(2n+1)-流形中的一些基本知識,其次主要考慮一個滿足CR次Laplacian比較定理并且具有m-Bakry-Emery(或∞-Bakry-Emery)偽Hermitian Ricci曲率條件的完備非緊偽Hermitian(2n + 1)-流形,得到了該流形上的非線性次拋物方程的正解的次梯度估計.
[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，

本文編號：2035693