Mapping Problems,Fundamental Groups and Defect Measures

作     者：Fanghua LinCourant Institute of Mathematics,New York University,New York,NY 10012,USA 

作者机构：Courant Institute of Mathematics New York University New York USA 

出 版 物：《Acta Mathematica Sinica,English Series》 (数学学报（英文版）)

年 卷 期：1999年第15卷第1期

页      面：25-52页

核心收录：

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

基　　金：Partially supported by NSF Grant DMS 9626166 

主　　题：Defect measure Harmonic mapping Generalized varifold Rectifiability 

摘      要：We study all the possible weak limits of a minimizing sequence,for p-energy functionals, consisting of continuous maps between Riemannian manifolds subject to a Dirichlet boundary condition or a homotopy *** show that if p is not an integer,then any such weak limit is a strong limit and,in particular,a stationary p-harmonic map which is C1,α continuous away from a closed subset of the Hausdorff dimension ≤n-[p]-*** p is an integer,then any such weak limit is a weakly p-harmonic map along with a（n-p）-rectifiable Radon measure μ.Moreover,the limiting map is C1,α continuous away from a closed subset ∑=spt μ∪S with Hn-p（S）=***,we discuss the possible varifolds type theory for Sobolev mappings.