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    Please use this identifier to cite or link to this item: http://nthur.lib.nthu.edu.tw/dspace/handle/987654321/86587


    Title: 完備流形上的調和映射
    Authors: 鄭穎鍾
    Cheng, Ying-Chung
    Description: GH02101021606
    碩士
    數學系
    Date: 2014
    Keywords: 調和映射
    harmonic maps
    Abstract: 此篇論文中含有兩個主題,一是p-調和映射的凸集合叢簇性質,另一是在有Weighted Poincare'不等式的完備流形上的Lioville定理。
    1.p-調和映射的凸集合叢簇性質:
    在這篇論文中,我們介紹了從完備流形到Cartan-Hadamard的p-調和映射,並且估計其值域。我們也給出了相異massive集合最大數量的上界。

    2.在有Weighted Poincare'不等式的完備流形上的Lioville定理:
    令M是一個有下界Ricci曲率的完備非緊緻流形,N是一個有非正sectional曲率的完備流形。假設Weighted Poincare'不等式成立與Dirichlet能量函數有適當成長的話,我們證明了從M到N的調和映射之Liouville性質。
    There are two topics in this paper. One is Convex Hull Property of p-harmonic maps, and the other is Liouville theorems on manifolds with weighted poincare' inequality.
    1.Convex Hull Property Of P-harmonic Maps:
    In this paper, we introduce the p-harmonic maps on complete manifolds to Cartan-Hadamard manifolds and estimate the image of the maps. We give the upper bound for the maximum number of disjoint massive sets.

    2.Liouville Theorems On Manifolds With Weighted Poincare' Inequality:

    Let M be a complete noncompact manifold with some Ricci curvature lower bound and N be a complete manifold with nonpositive sectional curvature. We prove the Liouville property on harmonic maps from M to N provided that the weighted Poincare' inequality holds and the Dirichlet energy function of the harmonic map has a proper growth.
    URI: http://nthur.lib.nthu.edu.tw/dspace/handle/987654321/86587
    Source: http://thesis.nthu.edu.tw/cgi-bin/gs/hugsweb.cgi?o=dnthucdr&i=sGH02101021606.id
    Appears in Collections:[數學系] 博碩士論文

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