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

Absos Ali Shaikh; Chandan Kumar Mondal; Izhar Ahmad

doi:10.1016/j.geomphys.2019.02.006

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

Absos Ali Shaikh^*, Chandan Kumar Mondal, Izhar Ahmad

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

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 functions 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 an inequality related with convex function.

Original language	English
Pages (from-to)	104-110
Number of pages	7
Journal	Journal of Geometry and Physics
Volume	140
DOIs	https://doi.org/10.1016/j.geomphys.2019.02.006
State	Published - Jun 2019

Bibliographical note

Publisher Copyright:
© 2019 Elsevier B.V.

Keywords

Convex function
Even convex function
Manifold with a pole
Negative point of a manifold
Odd convex function

ASJC Scopus subject areas

Mathematical Physics
General Physics and Astronomy
Geometry and Topology

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10.1016/j.geomphys.2019.02.006

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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 functions 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 an inequality related with convex function.",

keywords = "Convex function, Even convex function, Manifold with a pole, Negative point of a manifold, Odd convex function",

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AU - Shaikh, Absos Ali

AU - Mondal, Chandan Kumar

AU - Ahmad, Izhar

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N2 - 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 functions 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 an inequality related with convex function.

AB - 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 functions 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 an inequality related with convex function.

KW - Convex function

KW - Even convex function

KW - Manifold with a pole

KW - Negative point of a manifold

KW - Odd convex function

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JF - Journal of Geometry and Physics

ER -

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

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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