Hyperelliptic surfaces are Loewner |
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| Authors: | Mikhail G. Katz Sté phane Sabourau |
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| Affiliation: | Department of Mathematics and Statistics, Bar Ilan University, Ramat Gan 52900, Israel ; Laboratoire de Mathématiques et Physique Théorique, Université de Tours, Parc de Grandmont, 37400 Tours, France |
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| Abstract: | We prove that C. Loewner's inequality for the torus is satisfied by conformal metrics on hyperelliptic surfaces  as well. In genus 2, we first construct the Loewner loops on the (mildly singular) companion tori, locally isometric to  away from Weierstrass points. The loops are then transplanted to  , and surgered to obtain a Loewner loop on  . In higher genus, we exploit M. Gromov's area estimates for  -regular metrics on  . |
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| Keywords: | $varepsilon$-regular metrics Hermite constant hyperelliptic involution Loewner inequality Pu's inequality systole Weierstrass point |
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