2 problems

For a geodesic polygon in a black-hole spacetime, let $\mathring{\alpha}_{M}$ denote its Gaussian bending measure, and suppose that all vertices lie at the same distance $d$ from t…

Let $(M,g)$ be a two-dimensional Riemannian manifold, let $P$ be a compact geodesic polygon in $M$, and let $p$ be a corner of $P$ with interior angle $\gamma\in(0,2\pi]$. Write…