We are concerned with a super-Liouville equation on compact surfaces with genus larger than one, obtaining the first non-trivial existence result for this class of problems via min-max methods. In particular we make use of a Nehari manifold and, after showing the validity of the Palais-Smale condition, we exhibit either a mountain pass or linking geometry.

中文翻译：

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紧曲面上超刘维尔方程的存在性结果

我们关注的是在类大于 1 的紧曲面上的超刘维尔方程，通过 min-max 方法获得此类问题的第一个非平凡存在结果。特别是我们利用了 Nehari 流形，在证明了 Palais-Smale 条件的有效性之后，我们展示了山口或连接几何。