We consider properties of the total absolute geodesic curvature functional on circle immersions into a Riemann surface. In particular, we study its behavior under regular homotopies, its infima in regular homotopy classes, and the homotopy types of spaces of its local minima. We also consider the total curvature functional on the space of 2-sphere immersions into 3-space in a similar spirit. We...

Charles Evans We present an exposition of various results dealing with the total curvature of curves in Euclidean 3-space. There are two primary results: Fenchel’s theorem and the theorem of Fary and Milnor. Fenchel’s theorem states that the total curvature of a simple closed curve is greater than or equal to 2π, with equality if and only if the curve is planar convex. The Fary-Milnor theorem s...

scape bending disorder is the most important factor affecting postharvest loss of gerbera cut flowers. one of the ultimate reasons for gerbera stem bending is lignin, with deformation structural functions and defensive mechanisms. this postharvest experiment was conducted to evaluate the role of phenylalanine ammonia lyase (pal) and peroxidase (pod) enzymes activity in stem bending of two gerbe...