Mathematics – Differential Geometry
Scientific paper
2010-01-25
Mathematics
Differential Geometry
14 pages, some typos are corrected and some proofs are written in more detail
Scientific paper
Let $g=(g_{ij})$ be a complete Riemmanian metric on $\R^2$ with finite total area and $I_g=\inf_{\gamma}I(\gamma)$ with $I(\gamma)=L(\gamma)(A_{in}(\gamma)^{-1}+A_{out}(\gamma)^{-1})$ where $\gamma$ is any closed simple curve in $\R^2$, $L(\gamma)$ is the length of $\gamma$, $A_{in}(\gamma)$ and $A_{out}(\gamma)$ are the area of the regions inside and outside $\gamma$ respectively, with respect to the metric $g$. We prove the existence of a minimizer for $I_g$. As a corollary we obtain a new proof for the existence of a minimizer for $I_{g(t)}$ for any $0
No associations
LandOfFree
Minimizer of an isoperimetric ratio on a metric on $\R^2$ with finite total area does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Minimizer of an isoperimetric ratio on a metric on $\R^2$ with finite total area, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Minimizer of an isoperimetric ratio on a metric on $\R^2$ with finite total area will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-129946