# Width estimate and doubly warped product

@article{Zhu2020WidthEA, title={Width estimate and doubly warped product}, author={Jintian Zhu}, journal={arXiv: Differential Geometry}, year={2020} }

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…

## 19 Citations

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