Abstract It is known that ground states of the pseudo-relativistic Boson stars exist if and only if the stellar mass N > 0 satisfies N N ⁎ , where the finite constant N ⁎ is called the critical stellar mass. Lieb and Yau conjecture in [Comm. Math. Phys., 1987] that ground states of the pseudo-relativistic Boson stars are unique for each N N ⁎ . In this paper, we prove that the above uniqueness conjecture holds for the particular case where N > 0 is small enough.

中文翻译：

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伪相对论玻色子星基态的 Lieb-Yau 猜想

摘要 众所周知，当且仅当恒星质量 N > 0 满足 NN ⁎ 时，伪相对论玻色子星的基态才存在，其中有限常数 N ⁎ 称为临界恒星质量。Lieb 和 Yau 猜想 [Comm. 数学。Phys., 1987] 认为伪相对论玻色子星的基态对于每个 NN ⁎ 都是唯一的。在本文中，我们证明了上述唯一性猜想适用于 N > 0 足够小的特殊情况。