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arXiv · 1807.02708

On open flat sets in spaces with bipolar comparison

Nina Lebedeva
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Abstract

We show that if a Riemannian manifold satisfies (3,3)-bipolar comparisons and has an open flat subset then it is flat. The same holds for a version of MTW where the perpendicularity is dropped. In particular we get that the (3,3)-bipolar comparison is strictly stronger than the Alexandrov comparison.

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Nina Lebedeva. 2018-07-07. On open flat sets in spaces with bipolar comparison. https://arxiv.org/abs/1807.02708

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