3 problems

Let $(M,g)$ be a simple Riemannian manifold with boundary defining function $\rho$, and fix $\gamma>-1$. An $\alpha$-boundary defining function ($\alpha$-bdf) for $\partial_+SM$ is…

Let $(M,g)$ be a simple Riemannian manifold with boundary defining function $\rho$. For $\boldsymbol{t}$ an $b1$-boundary defining function on $b4_+SM$, let $I_0$ denote the geodes…

X-ray endpoint conjecture. For every $\varepsilon>0$, there is a constant $C_\varepsilon<\infty$ such that