Horizons of fractional Brownian surfaces

We investigate the conjecture that the horizon of an index-alpha fractional Brownian surface has (almost surely) the same Holder exponents as the surf ace itself, with corresponding relationships for fractal dimensions. We est ablish this formally for the usual Brownian surface (where alpha = 1/2), an d also for other alpha, 0 < alpha < 1, assuming a hypothesis concerning max ima of index-etc Brownian motion. We provide computational evidence that th e conjecture is indeed true for all alpha.