4 problems

Let $L_\kappa=-\partial_s^2+\kappa^2$ be the Schrödinger operator associated with an elastica, where $\kappa$ denotes its curvature. Lowest-eigenvalue conjecture. The lowest eigenv…

The elastica model describes DNA shapes through solutions of the focusing modified Korteweg–de Vries (MKdV) equation on hyperelliptic curves, with reality conditions restricting wh…

Global optimizer conjecture. There is a number $\xi(j)\in(0,1)$ such that the globally least bent confined elastica is a $j$-$(j+1)$-clew if $r_L/R<j+\xi$, while the global optimiz…

Let $E$ be the limiting functional obtained as the … -convergence, compactness of minimizers under the same boundedness constraint, and a sufficient condition for global optimizati…