The growth of the Martin kernel in a horn-shaped domain Dante DeBlassie 31C3531C0535C2060J50horn-shaped domainMartin kernel at infinitygrowth rate at infinitysmall perturbations$h$-transform If a horn-shaped domain in $\mathbb{R}^{d+1}$ does not open too rapidly at $\infty$, then the Martin boundary (with respect to the Laplacian) at $\infty$ is homeomorphic to the sphere $S^{d-1}$. Given a point $\varphi$ in the sphere, we determine the growth rate of the Martin kernel with pole at $\varphi$ explicitly in terms of the speed at which the horn opens at $\infty$. Indiana University Mathematics Journal 2008 text pdf 10.1512/iumj.2008.57.3392 10.1512/iumj.2008.57.3392 en Indiana Univ. Math. J. 57 (2008) 3115 - 3130 state-of-the-art mathematics http://iumj.org/access/