Complete hyperelliptic integrals of the first kind and their non-oscillation

Lubomir Gavrilov, Iliya D. Iliev

Let $P(x)$ be a real polynomial of degree $2g+1$, $H=y^2+P(x)$ and $\delta (h)$ be an oval contained in the level set $\{H=h\}$. We study complete Abelian integrals of the form $$I(h)=\i…