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On the conformal volume of 2-tori

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arxiv 1507.01485 v2 pith:RRK2SEDH submitted 2015-07-06 math.DG

Robert L. Bryant This is my paper · ORCID
classification math.DG
keywords proofconformaltorivolumeclaimconjecturemontieloriginally
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This note (originally from 2015) provides a proof of a 1985 conjecture of Montiel and Ros concerning the conformal volume of tori. This updated version adds a proof of the claim made in Remark 5 about the value of the conformal volume of tori in the cases not covered by the conjecture of Montiel and Ros. Originally, I did not think that this claim was of enough interest to warrant including the (somewhat involved) proof, but time has shown otherwise. (Also, the proof included here is shorter than my original proof; instead, it relies on a MAPLE computation.)

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  1. On Berger's Isoperimetric Problem

    math.DG 2025-06 conditional novelty 4.0 of 10

    Using conformal area results, the paper reproves that the flat equilateral torus maximizes the first eigenvalue among all tori and derives an improved upper bound.

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