  We investigate the "hot--spots" property for the survival time probability of
Brownian motion with killing and reflection in planar convex domains whose
boundary consists of two curves, one of which is an arc of a circle,
intersecting at acute angles. This leads to the "hot--spots" property for the
mixed Dirichlet--Neumann eigenvalue problem in the domain with Neumann
conditions on one of the curves and Dirichlet conditions on the other
