07-53 Pavel Exner, Martin Fraas, Evans M. Harrell II
On the critical exponent in an isoperimetric inequality for chords (209K, pdf) Mar 5, 07
Abstract , Paper (src), View paper (auto. generated pdf), Index of related papers

Abstract. The problem of maximizing the $L^p$ norms of chords connecting points on a closed curve separated by arclength $u$ arises in electrostatic and quantum--mechanical problems. It is known that among all closed curves of fixed length, the unique maximizing shape is the circle for $1 \le p \le 2$, but this is not the case for sufficiently large values of $p$. Here we determine the critical value $p_c(u)$ of $p$ above which the circle is not a local maximizer finding, in particular, that $p_c(\frac12 L)=\frac52$. This corrects a claim made in \cite{EHL}.

Files: 07-53.src( 07-53.keywords , LeakyIn6b.pdf.mm )