Solution
= Solution
For $v\in T_p\Sigma$, let $\gamma_v$ be the maximal geodesic with $\gamma_v(0)=p$, $\dot\gamma_v(0)=v$. Then $\exp_p(v)=\gamma_v(1)$ on the open star-shaped set of $v$ for which time $1$ exists.
= Solution
For $v\in T_p\Sigma$, let $\gamma_v$ be the maximal geodesic with $\gamma_v(0)=p$, $\dot\gamma_v(0)=v$. Then $\exp_p(v)=\gamma_v(1)$ on the open star-shaped set of $v$ for which time $1$ exists.