Polynomial growth of subharmonic functions in a strongly symmetric Riemannian manifold

Absos Ali Shaikh; Chandan Kumar Mondal

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arXiv · 1806.07215

Polynomial growth of subharmonic functions in a strongly symmetric Riemannian manifold

Absos Ali Shaikh·Chandan Kumar Mondal

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Abstract

In this article we have studied some properties of subharmonic functions in a strongly symmetric Riemannian manifold with a pole. As a generalization of polynomial growth of a function we have introduced the notion of polynomial growth of some degree of a function with respect to a real function and proved that any non-negative twice differentiable subharmonic functions in an $n$-dimensional manifold always admit polynomial growth of degree $1$ with respect to a non-negative real valued subharmonic function on real line. We have also given a lower bound of the integration of a convex function in a geodesic ball.

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Absos Ali Shaikh, Chandan Kumar Mondal. 2018-06-19. Polynomial growth of subharmonic functions in a strongly symmetric Riemannian manifold. https://arxiv.org/abs/1806.07215

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