标题： 紧性与球面上超黎曼方程的最小能量解 显示英文标题

标题： Compactness and least energy solutions to the super-Liouville equation on the sphere

摘要： 在本工作中，我们研究球面上带有正系数函数的超-Liouville方程。 我们首先推导方程旋量部分的估计，从而发现解的旋量部分的能量是均匀有界的。 然后从两个方面分析解空间的紧性：能量较小的解的紧性和关于球面共形变换群的紧性。 最后，通过引入一个新的自然约束——Nehari流形，并采用变分方法，在系数函数为偶函数的情况下，得到了最小能量解的存在性。 显示英文摘要

摘要： In this work, we study the super-Liouville equation on the sphere with positive coefficient functions. We begin by deriving estimates for the spinor component of the equation, thereby finding that the energy of the spinor part of solutions is uniformly bounded. We then analyze the compactness of the solution space in two aspects: the compactness for solutions with small energy and the compactness with respect to the conformal transformation group of the sphere. Finally, by introducing a new natural constraint, the Nehari manifold, and employing variational methods, we obtain the existence of the least energy solutions when the coefficient functions are even.