Hello i have this question:
Let $S$ be a $CAT(1)$-surface, and $\Delta$ a triangle on it, do some one have an idea or a reference about how to prove that $\alpha+\beta+\gamma-\pi\leq area(\Delta)$
where $\alpha,\beta,\gamma$ are the angles of the triangle in the Alexandrov sense and $area(\Delta)$ is the 2-dimensional Hausdorff measure given by the CBA(1) metric.
Thanks for any answer