Want site search autocompletion? See here Encountering 429 Too Many Requests errors when browsing the site? See here
A metric space M {\displaystyle M} equipped with a metric d {\displaystyle d} .
A path γ : [ 0 , 1 ] → M {\displaystyle \gamma :[0,1]\to M} is termed a minimizing geodesic if it is the shortest path from γ ( 0 ) {\displaystyle \gamma (0)} to γ ( 1 ) {\displaystyle \gamma (1)} .
By shortest, we mean path of minimum length where the length of a path is defined as:
lim sup 0 = t 0 ≤ t 1 ≤ t 2 ≤ … ≤ t n = 1 ∑ i d ( γ ( t i ) , γ ( t i + 1 ) {\displaystyle \lim \sup _{0=t_{0}\leq t_{1}\leq t_{2}\leq \ldots \leq t_{n}=1}\sum _{i}d(\gamma (t_{i}),\gamma (t_{i+1})}
equipped with a metric 
.
![{\displaystyle \gamma :[0,1]\to M}](https://wikimedia.org/api/rest_v1/media/math/render/svg/0066953642fb00abb394327531cea098815cd1c8)
is termed a minimizing geodesic if it is the shortest path from 
to 
.
