September 15, 3:30 Wed. Kerchof 326
L. Thomas
"Lower bound for a Schrodinger operator defined by curvature on a
closed loop"
Let H(k)= -d^2/ds^2+k(s)^2 be a one-dimensional Schrodinger
operator with potential V(s)= k(s)^2, where k(s) is the curvature of a
closed curve (in two or three dimensions). We consider the conjecture
that for curves of total length 2xpi, H(k)\geq 1 and describe a local result.
This will be the first of two talks, the other given by
A. Burchard, who will describe a connection between the conjecture and
a conjectured best constant for a Lieb-Thirring inequality, this
connection discovered by Benguria and Loss.