Title: Variation of maximal operators of convolution type
Abstract: We will study the action of several maximal operators of convolution type, associated to elliptic and parabolic equations, on BV functions and Sobolev functions in the euclidian space $\mathbb{R}^d$, the sphere $\mathbb{S}^d$ and the torus $\mathbb{T}^d$, and establish a variation-diminishing behavior for these operators. The crucial regularity property that these maximal functions share is that they are subharmonic in the corresponding detachment sets. Joint work with E. Carneiro and R. Finder. (preprint at http://arxiv.org/abs/1512.02715)