Are circles isoperimetric in the plane with density e?
نویسندگان
چکیده
We prove that an isoperimetric region in R2 with density er must be convex and contain the origin, and provide numerical evidence that circles about the origin are isoperimetric, as predicted by the Log-Convex Density Conjecture. Acknowledgements: We thank our advisor Frank Morgan for his patience and invaluable input. We also thank Diana Davis, Sean Howe and Michelle Lee for their help. For his helpful comments, we would like to thank our anonymous referee. For funding, we thank the National Science Foundation for grants to Prof. Morgan and to the Williams College “SMALL” Research Experience for Undergraduates, Williams College for additional funding, and the Mathematical Association of America for supporting our trip to speak at MathFest 2011. RHIT Undergrad. Math. J., Vol. 16, No. 1 Page 209
منابع مشابه
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