A construction of patterns with many critical points on topological tori

Putri Zahra Kamalia, Shigeru Sakaguchi

Published 2019-12-04Version 1

We consider reaction-diffusion equations on closed surfaces in $\mathbb R^3$ having genus $1$. Stable nonconstant stationary solutions are often called patterns. The purpose of this paper is to construct closed surfaces together with patterns having as many critical points as one wants.