2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/57653To determine the sharp constants for the one dimensional Lieb--Thirring inequalities with exponent gamma in (1/2,3/2) is still an open problem. According to a conjecture by Lieb and Thirring the sharp constant for these exponents should be attained by potentials having only one bound state. Here we exhibit a connection between the Lieb--Thirring conjecture for gamma=1 and an isporimetric inequality for ovals in the plane.9 pages, LaTexMathematical Physics81Q10 (primary), 53A04, 49R50 (secondary)text