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The isoperimetric profile of infinite genus surfaces

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Abstract

It is known that if the isoperimetric profile of a finite genus non-compact surface grows faster than \({\sqrt{t}}\) , then it grows at least as a linear function. In other words there are ‘gaps’ in the isoperimetric profile of surfaces with finite genus. In this paper we show that no gap exists for surfaces of infinite genus.

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  1. Mathematics Department, University of Athens, 157 84, Athens, Greece

    Procopis Psaltis

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  1. Procopis Psaltis
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Correspondence to Procopis Psaltis.

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Psaltis, P. The isoperimetric profile of infinite genus surfaces. Geom Dedicata 149, 95–102 (2010). https://doi.org/10.1007/s10711-010-9468-9

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  • DOI: https://doi.org/10.1007/s10711-010-9468-9

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