The Monotonicity Of Ratios Of Some Abelian Integrals

In this paper, we study the monotonicity of the ratio of the Abelian integrals, closed integral(gamma i(h)) ydx and closed integral(gamma i(h)) xydx, in an interval, where i = 1, 2, and gamma(i)(h) is a compact component of some hyperelliptic curves with genus 2a s h is an element of gamma(i)(h). We give positive answers to the two conjectures proposed by Wang et al. (2014) [18]. (c) 2020 Elsevier Masson SAS. All rights reserved.