Bolza surface; elliptic integrals; Extremal length; Landen transformations; systole; Algebra and Number Theory; Analysis; Geometry and Topology; Statistics and Probability
Abstract :
[en] We prove that the extremal length systole of genus two surfaces attains a strict local maximum at the Bolza surface, where it takes the value√2.
Disciplines :
Mathematics
Author, co-author :
Fortier Bourque, Maxime; Département de mathématiques et de statistique, Université de Montréal, Montréal, Canada
MARTINEZ GRANADO, Didac ; University of Luxembourg > Faculty of Science, Technology and Medicine (FSTM) > Department of Mathematics (DMATH)
Vargas Pallete, Franco; Institut des Hautes Études Scientifiques, Bures-sur-Yvette, France
External co-authors :
yes
Language :
French
Title :
LA SYSTOL E DE LONGUEUR EXTRÉMALE DE LA SURFACE DE BOLZA
Alternative titles :
[en] The extremal length systole of the Bolza surface
D\u00EDdac Mart\u00EDnez-Granado was supported by the Luxembourg National research Fund AFR/Bilateral-ReSurface 22/17145118. Franco Vargas Pallete\u2019s research was supported by NSF grant DMS-2001997. Part of this material is also based upon work supported by the National Science Foundation under Grant No. DMS-1928930 while Franco Vargas Pallete participated in a program hosted by the Mathematical Sciences Research Institute in Berkeley, California, during the Fall 2020 semester.Keywords: Extremal length, systole, Bolza surface, elliptic integrals, Landen transformations. 2020 Mathematics Subject Classification: 31A15, 30F60, 57K20. DOI: https://doi.org/10.5802/ahl.223 (*) D\u00EDdac Mart\u00EDnez-Granado was supported by the Luxembourg National research Fund AFR/Bilateral-ReSurface 22/17145118. Franco Vargas Pallete\u2019s research was supported by NSF grant DMS-2001997. Part of this material is also based upon work supported by the National Science Foundation under Grant No. DMS-1928930 while Franco Vargas Pallete participated in a program hosted by the Mathematical Sciences Research Institute in Berkeley, California, during the Fall 2020 semester.
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