Abstract This paper concerns the critical points of a class of degenerate elliptic operators. We prove that the nonexistence of critical point of the Green function for the Kohn-Laplacian of an H-star-shaped region on the first Heisenberg group. Moreover, we prove that solutions to a class of semi-linear degenerate elliptic equations on an H-star-shaped ring have no critical point.

中文翻译：

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海森堡群上亚椭圆方程解的临界点

摘要 本文研究一类退化椭圆算子的临界点。我们证明了第一海森堡群上一个H星形区域的Kohn-Laplacian格林函数的临界点不存在。此外，我们证明了一类半线性退化椭圆方程在 H 星形环上的解没有临界点。