I'm reading a paper, in which we have $M^n$ an n-dimensional compact hypersurface embedded in $\mathbb{R}^{n+1}$. We take the scalar cuvature $R$ to be the elementary symmetric polynomial of degree 2 in the principal curvatures of $M$. We know that $R$ is constant.


The author then says "As $M$ has one elliptic point, $R$ is a positive constant and the mean curvature is positive somewhere".


I'm lost here - Why does $M$ have an elliptic point? And how does this affect $R$ and the mean curvature?


Thanks for any help.



Hypersurfaces and Elliptic Points
Elliptic point is, by definition, a point where all the principal curvatures are positive, hence $R$ is positive. A point of maximal distance from some far-away basepoint is elliptic.


