講題：Stabilization technique applied on curve shortening flow in R^2 and R^3.
Abstract:
First we apply the stabilization technique, developed by T. Zelenyak in 1960s for parabolic equations, on the curve shortening flow in R^2, and derive a new monotonicity formula with logarithmic terms. Then we use this idea and derive several new monotonicity formulas for the CSF in R^3. All of them share one main feature: the dependence of the “energy” term on the angle between the position vector and the plane orthogonal to the tangent vector. The first formula deals with the projection of the curve on the unit sphere, and computes the derivative of its length. The second formula is the generalization of the classical formula of G. Huisken, while the third one is the generalization of the monotonicity formula with logarithmic terms mentioned above in R^3.