Abstract
We establish an isoperimetric inequality for the first non-zero eigenvalue of the Laplace operator on the surface of genus one and of a fixed area.
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Supported by the Federal Ministry of Science and Research, Austria. This work was done while the author was visiting IHES, Bures-sur-Yvette and ESI, Vienna. I thank these institutes for their hospitality.
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Nadirashvili, N. Berger's isoperimetric problem and minimal immersions of surfaces. Geometric and Functional Analysis 6, 877–897 (1996). https://doi.org/10.1007/BF02246788
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DOI: https://doi.org/10.1007/BF02246788