This is an announcement for the paper “Mankiewicz's theorem and the Mazur--Ulam property for $C^*$-algebras” by Michiya Mori<https://arxiv.org/search?searchtype=author&query=Mori%2C+M>, Narutaka Ozawa<https://arxiv.org/search?searchtype=author&query=Ozawa%2C+N>. Abstract: We prove that every unital $C^*$-algebra $A$, possibly except for the $2$ by $2$ matrix algebra, has the Mazur--Ulam property. Namely, every surjective isometry from the unit sphere $S_A$ of $A$ onto the unit sphere $S_Y$ of another normed space $Y$ extends to a real linear map. This extends the result of A. M. Peralta and F. J. Fernandez-Polo who have proved the same under the additional assumption that both $A$ and $Y$ are von Neumann algebras. In the course of the proof, we strengthen Mankiewicz's theorem and prove that every surjective isometry from a closed unit ball with enough extreme points onto an arbitrary convex subset of a normed space is necessarily affine. The paper may be downloaded from the archive by web browser from URL https://arxiv.org/abs/1804.10674