关于Q-曲率流的几个注记  

Remarks on the Q-curvature flow

作　　者：陈学长[1,2] 马力[3] 徐兴旺 

机构地区：[1]北京大学北京国际数学研究中心,北京100871 [2]南京大学数学系,南京210093 [3]河南师范大学数学系,新乡453007 [4]Department of Mathematics,National University of Singapore

出　　处：《中国科学：数学》2014年第2期183-192,共10页Scientia Sinica：Mathematica

基　　金：国家自然科学基金(批准号:11201223和11271111);中国博士后研究基金(批准号:2011M500175);南京大学思源基金;National University of Singapore research funds(批准号:R-146-000-169-112)资助项目

摘　　要：标准球面上的预定纯量曲率问题已经得到很好的研究,为此,几种不同的方法发展起来了.它的高维对应的问题即预定Q-曲率问题也吸引了众多人的注意.负梯度流的方法在处理此类问题上似乎十分有效,至少在曲率备选函数是正的情形下是如此的.本文的目的在于指出,对于指数非线性增长的预定Q-曲率问题,Q-曲率备选函数的正性假设是不必要的.The prescribing scalar curvature problem on the standard sphere has been well studied and several methods have been developed for this purpose. Its higher order analogy problem, namely the prescribing Q- curvature problem has also attracted a lot of attention. The negative gradient flow method seems very well suitable to those type of problem, at least for the case where the prescribing curvature candidate is positive. The main aim of the current note is to point out that in the prescribing Q-curvature problem with exponential non-linearity, the positivity of the curvature candidate is not necessary.

关 键 词：Q-曲率流 爆破分析Morse理论 

分 类 号：O186.11[理学—数学]