Abstract

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

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