Inscribed and circumscribed radius of $κ$-convex hypersurfaces in Hadamard manifolds

Alexander A. Borisenko, Vicente Miquel

Published 2023-07-18Version 1

Let $P$ be a convex polygon in a Hadamard surface $M$ with curvature $K$ satisfying $-k_2^2 \ge K \ge -k_1^2$. We give an upper bound of the circumradius of $P$ in terms of a lower bound of the curvature of $P$ at its vertices.