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arXiv · 1806.07234

Non-existence of certain type of convex functions on a Riemannian manifold with a pole

Absos Ali Shaikh·Chandan Kumar Mondal·Izhar Ahmad
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Abstract

This paper is devoted to the study of non-existence of certain type of convex functions on a Riemannian manifold with a pole. To this end, we have developed the notion of odd and even function on a Riemannian manifold with a pole and proved the non-existence of non-trivial and non-negative differentiable odd convex function whose gradient is complete. Finally, we have deduced some isoperimetric type inequality related with convex function.

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Absos Ali Shaikh, Chandan Kumar Mondal, Izhar Ahmad. 2018-06-19. Non-existence of certain type of convex functions on a Riemannian manifold with a pole. https://doi.org/10.1016/j.geomphys.2019.02.006

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