Title: Quantitative Alexandrov theorem and its applications in the volume preserving mean curvature flow
Abstract: A classical theorem in differential geometry, Alexandrov Theorem, states that if Σ is a closed connected embedded smooth surface in R^n (n ≥ 3) with constant mean curvature, then it is a round sphere. In this talk, a new quantitative version of it will be given in R^3. Using it we obtain a result on the asymptotic behaviour of weak solutions for the volume preserving mean curvature flow. Here, by weak solution we mean a flat flow, obtainedvia the minimizing movement scheme. The results discussed are obtained by a collaboration with V. Julin, M. Morini and E. Spadaro.
