关于凸情形下的Markus猜想
On the Markus conjecture in convex case
摘要：
本文证明了在自同构群的单位连通区的作用下，任何在边界上具有非空极限集的凸仿射域不能覆盖具有平行体积的紧致仿射流形，这是凸情形下Markus猜想的一个肯定回答.因此，我们证明了Markus猜想对维数为$\leq 5$的凸仿射流形成立.
英文摘要：
In this paper, we show that any convex affine domain with a nonempty limit sets on the boundary under the action of the identity component of the automorphism group cannot cover a compact affine manifold with a parallel volume, which is a positive answer to the Markus conjecture for convex case. Consequently, we show that the Markus conjecture is true for convex affine manifolds of dimension $\leq 5$.
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