THE ISOPERIMETRIC PROBLEM ON PLANES WITH DENSITY

書誌事項

公開日
2008-10
権利情報
  • https://www.cambridge.org/core/terms
DOI
  • 10.1017/s000497270800052x
公開者
Cambridge University Press (CUP)

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説明

<jats:title>Abstract</jats:title><jats:p>We discuss the isoperimetric problem in planes with density. In particular, we examine planes with generalized curvature zero. We solve the isoperimetric problem on the plane with density <jats:italic>e</jats:italic><jats:sup><jats:italic>x</jats:italic></jats:sup>, as well as on the plane with density <jats:italic>r</jats:italic><jats:sup><jats:italic>p</jats:italic></jats:sup> for <jats:italic>p</jats:italic><0. The Appendix provides a proof by Robert Bryant that the Gauss plane has a unique closed geodesic.</jats:p>

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