Stable and isoperimetric regions in rotationally symmetric tori with decreasing Gauss curvature Antonio Canete 49Q2049Q10stabilityisoperimetric problem In this work we classify the stable regions (second order minima of perimeter under an area constraint) in symmetric tori of revolution with piecewise continuous decreasing Gauss curvature from the longest parallel. For narrow standard tori of revolution, isoperimetric regions are disks, vertical annuli, or complements. Indiana University Mathematics Journal 2007 text pdf 10.1512/iumj.2007.56.3003 10.1512/iumj.2007.56.3003 en Indiana Univ. Math. J. 56 (2007) 1629 - 1659 state-of-the-art mathematics http://iumj.org/access/