The heat equation and harmonic maps of complete manifolds
The heat equation and harmonic maps of complete manifolds
复制标题
DOI：
10.1007/bf01232256
复制
发表时间：
1991-12
影响因子：
3.1
通讯作者：
Peter Li;Luen-Fai Tam
中科院分区：
文献类型：
--
作者：
Peter Li;Luen-Fai Tam
本文的主要目标是了解何时可以求解两个完全非紧流形之间的调和映射方程。具体来说，我们希望获得足够的条件来确保两个完全非紧流形之间具有有界能量密度的 C 1 映射 h 可以通过求解调和映射的抛物线方程平滑地变形为平滑的调和映射。对于我们的大多数应用来说，h 能量密度的假设是很自然的。事实上，众所周知，如果初始数据作为 R m 的函数增长得太快，即使是 R" 上的标准标量热方程也不具有唯一解。
The primary goal of this article is to understand when one can solve the harmonic map equation between two complete noncompact manifolds. Specifically, we would like to obtain sufficient conditions to ensure that a C 1 map, h, with bounded energy density between two complete noncompact manifolds can be deformed smoothly to a smooth harmonic map by solving the parabolic equation for harmonic maps. The assumption on the energy density of h is natural for most of our applications. In fact, it is known that even the standard scalar heat equation on R" does not have unique solution if the initial data grows too rapidly as a function of R m.