紧2-流形上的近视界几何方程（含g > 0的通解）
The Near Horizon Geometry Equation on Compact 2-Manifolds Including the General Solution for g > 0
摘要：
研究了紧致二维流形上具有宇宙学常数Λ的近视界几何（NHG）方程.证明了每个解在流形上的每一点都满足D型方程。在文献中已知的一个类似的结果是有效的，只有在一个适当的方式非退化点的一个给定的解决方案。在退化点，D型方程不适用。在本文中，我们证明了退化被排除的紧性。利用这一结果，我们找到了所有的解决方案，NHG方程的紧凑的2维流形的非正欧拉特征。在Λ = 0的情况下，一些已知的可积性条件被推广到任意值的Λ。它们对于正欧拉特征的紧致2-流形仍然是有用的。
英文摘要：
The Near Horizon Geometry (NHG) equation with a cosmological constant Λ is considered on compact 2-dimensional manifolds. It is shown that every solution satisfies the Type D equation at every point of the manifold. A similar result known in the literature was valid only for non-degenerate in a suitable way points of a given solution. At the degenerate points the Type D equation was not applicable. In the current paper we prove that the degeneracy is ruled out by the compactness. Using that result we find all the solutions to the NHG equation on compact 2-dimensional manifolds of non-positive Euler characteristics. Some integrability conditions known earlier in the Λ = 0 case are generalized to arbitrary value of Λ. They may be still useful for compact 2-manifolds of positive Euler characteristic.
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