On the Markus conjecture in convex case

2018/09/21 by Jo, Kyeonghee, Kim, Inkang
#FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.1809.07918

Abstract

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 ≤ 5.

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