I have a conceptual question: I know that the word "closed", depending on the context, can mean either the oposite of open or compact without boundary, but could the word "compact" mean compact without boudary?
This question is because I saw in a paper that $\int_M \Delta f dV=0$ where $f\in C^\infty(M)$ and $M$ is a compact minimal hypersurfaces of the Euclidean sphere.
No orientability assumption is assumed as well as any hypothesis about the boundary.
One more question: Does minimality imply orientability?