In this article, the authors in table 1 shows that for unduloid (that is rotation of an elliptic curve), shows that unduloid whether the meridian curvature (the profile curvature) is convex or concave have always same sign of mean curvature (which is positive in physical terms). I was trying to understand why?
in laplace equation we have:
$$-\frac{r''}{(1+r'^2)^{3/2}} + \frac{1}{r(1+r'^2)^{1/2}} = 2 H$$
the first term is the meridian principle curvature and the second one is the one along the circular cross section that is parallel to axis of revolution. the second term is always positive for $r>0$ and due to the fact it is circular so always convex. the first term might be negative or positive based on $r''$. Can we say then based on this table in this study that ellipses have curvatures always small than circles? Because it is not the case for nodoid, the competition between both give positive and negative mean curvature, but for unduloid is always positive, i don't find a good interpretation for this.