%0 Journal Article %@ 1531-3492 %A Baigent, S %D 2019 %F discovery:10049790 %I American Institute of Mathematical Sciences %J Discrete and Continuous Dynamical Systems - Series B %K Carrying simplex, convexity, concavity, May-Leonard map, invariant manifold %N 4 %P 1697-1723 %T Convex geometry of the carrying simplex for the May-Leonard map %U https://discovery.ucl.ac.uk/id/eprint/10049790/ %V 24 %X We study the convex geometry of certain invariant manifolds, known as carrying simplices, for 3-species competitive Kolmogorov-type maps. We show that if all planes whose normal bundles are contained in a fixed closed and solid convex cone are rendered convex (concave) surfaces by the map, then, if there is a carrying simplex, it is a convex (concave) surface. We apply our results to the May-Leonard map. %Z This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions.