论文标题
Kazdan-Warner在表面上问题的两种解决方案
Two solutions to Kazdan-Warner's problem on surfaces
论文作者
论文摘要
在本文中，我们在二维封闭的Riemannian歧管上研究了签名改变的卡兹丹 - 瓦纳问题，负欧拉数$χ（m）<0 $。我们表明，一次，凸集集合的直接方法用于找到相应功能的最小化器，然后通过使用山间通道的变异方法，可以使用另一种解决方案。总而言之，我们表明，如果规定的函数更改符号和平均负面，则至少有两种解决卡兹丹 - 瓦纳问题的解决方案。
In this paper, we study the sign-changing Kazdan-Warner's problem on two dimensional closed Riemannian manifold with negative Euler number $χ(M)<0$. We show that once, the direct method on convex sets is used to find a minimizer of the corresponding functional, then there is another solution via a use of the variational method of mountain pass. In conclusion, we show that there are at least two solutions to the Kazdan-Warner's problem on two dimensional Kazdan-Warner equation provided the prescribed function changes signs and with this average negative.
