Width estimate and doubly warped product

@article{Zhu2020WidthEA,
  title={Width estimate and doubly warped product},
  author={Jintian Zhu},
  journal={arXiv: Differential Geometry},
  year={2020}
}
  • Jintian Zhu
  • Published 3 March 2020
  • Mathematics
  • arXiv: Differential Geometry
In this paper, we give an affirmative answer to Gromov's conjecture ([3, Conjecture E]) by establishing an optimal Lipschitz lower bound for a class of smooth functions on orientable open $3$-manifolds with uniformly positive sectional curvatures. For rigidity we show that the universal covering of the given manifold must be $\mathbf R^2\times (-c,c)$ with some doubly warped product metric if the optimal bound is attained. This gives a characterization for doubly warped product metrics with… 

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