Abstract:
     The boundary Harnack principle dictates that every harmonic
     function vanishing on a segment of the boundary must decay at
     the same rate. We will discuss the techniques used to prove
     this principle for smooth Euclidean domains. While now the
     work of John Lewis and Kaj Nystr\"om have verified that this
     principle holds for more general Euclidean Lipschitz domains, their
     technique is not so readily available in more general metric
     measure spaces such as polarizable Carnot groups.