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arXiv · 2104.11429

Growth Competitions on Spherically Symmetric Riemannian Manifolds

Rotem Assouline
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Abstract

We propose a model for a growth competition between two subsets of a Riemannian manifold. The sets grow at two different rates, avoiding each other. It is shown that if the competition takes place on a surface which is rotationally symmetric about the starting point of the slower set, then if the surface is conformally equivalent to the Euclidean plane, the slower set remains in a bounded region, while if the surface is nonpositively curved and conformally equivalent to the hyperbolic plane, both sets may keep growing indefinitely.

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Rotem Assouline. 2021-04-23. Growth Competitions on Spherically Symmetric Riemannian Manifolds. https://doi.org/10.1515/agms-2022-0139

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