具有孤立奇点的 Yamabe 方程解的一种参数化
A Parametrization of Solutions to the Yamabe Equation with Isolated Singularity
AI总结：
本文受 Caffarelli 等人工作启发，证明了与调和函数对应的形式无穷级数可产生带不可去孤立奇点的 Yamabe 方程实际解，并提供了构造该类方程在孤立奇点及无穷远处所有解的通用方法。
摘要：
受 Caffarelli、Gidas 和 Spruck 一项开创性工作的启发，我们研究带有不可去孤立奇点的 Yamabe 方程的正解。已知，带有不可去孤立奇点的 Yamabe 方程解的集合与由调和函数确定的形式无穷级数对应的调和函数集合之间存在形式上的一一对应关系。本文中，我们证明这些形式无穷级数可产生带有不可去孤立奇点的 Yamabe 方程的实际解，这些解具有由对应调和函数确定的指定渐近行为。在更广泛的背景下，我们提供了一种通用方法，用于构造所有在孤立奇点附近的解以及所有在无穷远处的解。
英文摘要：
Inspired by a pioneering work by Caffarelli, Gidas, and Spruck, we study positive solutions to the Yamabe equation with nonremovable isolated singularities. It is known that there is a formal one-to-one correspondence between the collection of the solutions to the Yamabe equation with nonremovable isolated singularities and the collection of harmonic functions through formal infinite series determined by the harmonic functions. In this paper, we prove that these formal infinite series yield actual solutions to the Yamabe equation with a nonremovable isolated singularity. These solutions to the Yamabe equation have designated asymptotic behaviors determined by the harmonic functions. In a broader context, we provide a general method of constructing all solutions near their isolated singular points and all solutions near infinity.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
