Speaker: Mariana Smit Vega Garcia, Western Washington University
Title: Almgren type monotonicity formulas
Abstract: In this talk, we will explore the celebrated Almgren’s monotonicity formula. This beautiful result with far-reaching consequences states that if u is harmonic in the unit ball, then a certain frequency function N(r) is non-decreasing. Moreover, N(r) = k for all 0 < r < 1 if, and only if, u is homogeneous of degree k. We will then discuss some of the many applications of this formula, and recent developments connected to it. This is based on joint work with Blair Davey.