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On the Markus conjecture in convex case

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Abstract

In this paper, we show that any convex affine domain with a nonempty limit set 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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Acknowledgements

This work was done at Korea Institute for Advanced Study (KIAS) while the first author was a visiting professor in 2016-2017. The first author is grateful for the warm hospitality during her stay and acknowledges the partial support of NRF grant funded by the Korea government (MSIT) (NRF-2021R1F1A1049444). Both authors thank an anonymous referee for several insightful questions. The second author gratefully acknowledges the partial support of Grant NRF-2019R1A2C1083865 and KIAS Individual Grant (MG031408).

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  1. Division of Liberal Arts and sciences, Mokpo National Maritime University, Mokpo, Chonnam, 58628, Korea

    Kyeonghee Jo

  2. School of Mathematics, Korea Institute for Advanced Study, Seoul, 02455, Korea

    Inkang Kim

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  1. Kyeonghee Jo
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  2. Inkang Kim
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Correspondence to Inkang Kim.

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Jo, K., Kim, I. On the Markus conjecture in convex case. Ann Glob Anal Geom 60, 911–940 (2021). https://doi.org/10.1007/s10455-021-09796-z

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  • DOI: https://doi.org/10.1007/s10455-021-09796-z

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