Proceedings of the American Mathematical Society

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ISSN 1088-6826(e) ISSN 0002-9939(p)

Hyperelliptic surfaces are Loewner

Authors: Mikhail G. Katz and Stéphane Sabourau
Journal: Proc. Amer. Math. Soc. 134 (2006), 1189-1195
MSC (2000): Primary 53C23; Secondary 30F10
Posted: July 20, 2005
MathSciNet review: 2196056
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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 $\varepsilon$ -regular metrics on .

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