Bulletin des Sciences Mathématiques ( IF 1.241 ) Pub Date : 2020-11-18 , DOI: 10.1016/j.bulsci.2020.102934
Xianbo Sun; Na Wang; Pei Yu

In this paper, we study the monotonicity of the ratio of the Abelian integrals, ${\oint }_{{\gamma }_{i}\left(h\right)}ydx$ and ${\oint }_{{\gamma }_{i}\left(h\right)}xydx$, in an interval, where $i=1,2$, and ${\gamma }_{i}\left(h\right)$ is a compact component of some hyperelliptic curves with genus 2 as $h\in {\gamma }_{i}\left(h\right)$. We give positive answers to the two conjectures proposed by Wang et al. (2014) [18].

down
wechat
bug